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We're still in the midst of the third impeachment inquiry in US history, but most Americans seem to have already made up their minds.

In a new National Public Radio/PBS NewsHour poll, external, half of Americans say they approve of the impeachment inquiry - almost the same as last month.

Respondents are also roughly evenly split over whether Trump should be impeached and removed from office.

But a clear majority of Americans - 65% - say they can't imagine "any information or circumstances during the impeachment inquiry" actually changing their mind about impeachment.

Some 30% said it would be possible.

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And as BBC America Bureaux Editor Paul Danahar notes - even conservative outlets, like the president's favourite, Fox News, is noting the "quid pro quo".

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Sondland said his memory of a July call with President Trump was "triggered by someone's reference to A$AP Rocky", "the primary purpose" of the discussion.

In July, Trump asked that the US rapper be released from custody in Sweden, where he was charged with assault.

The repeated mentions of A$AP Rocky by the US Ambassador to the European Union stand out from typically dry impeachment hearing fodder - and the internet has noticed.

Google searches for the rapper have soared in the last few hours, beginning after Sondland arrived at Capitol Hill to testify.

Some online jokers are calling for A$AP Rocky to testify, even though he really has nothing to do with the impeachment inquiry.

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Republican lawyer Steve Castor pressed Sondland on why his first testimony to impeachment investigators made no mention of his phone call with Trump in which "investigations" were discussed.

Earlier, Sondland told the committee he recalled that the mobile phone call to Trump was initially placed from a Kyiv restaurant, and was held to discuss rapper A$AP Rocky, who at the time was in prison in Sweden.

"A phone call, for me, with the president of the United States or the president of fill-in-the-blank country, while people who get a call like that maybe once in a lifetime, a call like that might be very memorable.

"They might remember every single thing about it. I'm doing that all day long. And I'm not saying that in a way of being braggadocio or anything like that.

"But it's part of my routine day. So all of these calls, these meetings, with very important people tend to sort of blend together until I have someone who can show me what we discussed, what the subject was. Then all of a sudden it comes back."

US Vice-President Mike Pence's office has responded to Sondland's testimony that he voiced concerns to him about Ukraine aid being frozen.

His office says that alleged conversation "never happened".

Pence, who is in Wisconsin today, also retweeted House Republican leader Kevin McCarthy's criticism of the inquiry.

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Speaking to reporters on the South Lawn of the White House, the president moments ago reiterated that he doesn't really know Sondland.

"'What do you want from Ukraine?' he asks me," Trump says, reading from notes on Sondland's testimony.

"I keep hearing all these different ideas and theories. This is Ambassador Sondland speaking to me..."

"What do you want, what do you want? It was a very short and abrupt conversation he had with me."

"He's going, 'what do you want?' Here's my response. Ready? Got the camera's rolling? 'I want nothing. That's what I want from Ukraine.'"

"'I want nothing.' I said it twice!"

"I don't know him very well," Trump says of Sondland. "Seems like a nice guy, though."

The president repeats, reading from the testimony transcript: "I want nothing, I want no quid pro quo, tell President Zelensky to do the right thing."

The Republican lawyer Steve Castor is asking if Trump directly told Sondland about preconditions for a White House meeting with Zelensky.

No, says Sondland.

What about conditions for US military aid to be released?

No, says Sondland.

There's nothing regarding preconditions that ties anything "personally" to Trump, is there, asks the Republican.

"Personally? No."

Sondland says he was directed to work with Rudy Giuliani, Trump's personal lawyer. Castor asks why he thought Giuliani was speaking on behalf of Trump.

"Well, when the president says, 'talk to my personal attorney', and then Mr Giuliani - as his personal attorney - makes certain requests or demands, we assume it's coming from the president.

"I'm not testifying that I heard the president tell Giuliani to tell us, if that's your question."

Republicans are harping on that point, that Trump never "personally" directed Sondland to place preconditions on a White House meeting or US military aid.

Meanwhile, it looks like President Trump, who is said to be watching the hearing from the White House, is late departing for a scheduled trip to Texas, according to the BBC's Anthony Zurcher.

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On his call with Zelensky, the US president expressed interest in an idea that it was Ukraine - not Russia - meddling in the 2016 election.

The unsubstantiated theory holds that Ukrainian figures worked in concert with Democrats to undermine Trump's campaign.

They allege a hack on the Democratic National Committee in 2016 - which leaked politically embarrassing emails - was actually perpetrated by the Ukrainians and falsely blamed on the Russians.

The mention of "CrowdStrike" we heard earlier from the committee room referred to this conspiracy theory.

However, the US intelligence community has concluded that Russia, not Ukraine, interfered in the 2016 election.

The BBC's Kyiv correspondent Jonah Fisher explains how Ukraine became ensnared in these collusion claims here.

And our Reality Check team fact-checked the claims here.

Let's get our heads up for a moment.

Need a refresher on all things impeachment? We've got you covered.

SIMPLE GUIDE: If you want a basic take on what's going on, this one's for you

GO DEEPER: Here's a 100, 300 and 800-word summary of the story

WHAT'S IMPEACHMENT? It's a political process to remove a president - video guide

VIEW FROM COAL COUNTRY: Watch residents in West Virginia react

CONTEXT: Why Ukraine matters to the US

FACT-CHECK: Is the whistleblower linked to the Democrats?

Responding to questions from Democratic attorney Daniel Goldman, Sondland says he "never heard" directly from Trump that aid to Ukraine "was conditioned on the announcement of investigations".

"I don't recall President Trump ever talking to me about any security assistance, ever."

The statement will be seized upon by Trump's supporters as more proof there was no quid pro quo between the US president and Ukraine.

Still, Sondland stood by his claim that a link between aid to Ukraine and investigations sought by Giuliani and Trump was "abundantly clear to everyone".

The witness said in his opening statement that Giuliani "had demanded" Ukraine announce a Burisma investigation in return for US military aid.

But Congress can't impeach the president's lawyer.

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Sondland's testimony implicates Secretary of State Mike Pompeo, who had managed to keep his distance from this whole imbroglio.

The ambassador testified that his boss knew all about the alleged White House political pressure on the Ukrainians.

So where is Pompeo now?

Perhaps his ears have been burning as he attended a Nato foreign ministers' meeting in Brussels today.

America's top diplomat flies back to the US this afternoon. He may want to brace for turbulence.

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Anthony Zurcher
BBC North America reporter

With his opening statement to the House impeachment hearings on Wednesday, Gordon Sondland fired a torpedo that has blown a hole in the White House’s defences.

Water is rushing in, and it’s now a question of whether Republican senators will once again give Donald Trump a lifeboat before his presidency disappears beneath the waves.

Sondland, the US ambassador to the EU, was working with Donald Trump’s personal lawyer, Rudy Giuliani, on Ukrainian policy at the explicit direction of the president.

There was a quid-pro-quo.

A White House visit for Ukrainian President Volodymyr Zelensky was directly conditioned on publicly announcing opening investigations that could help the president politically. Sondland also came to believe that US military aid to Ukraine was also being held up for this reason.

Everyone at the White House - acting Chief of Staff Mick Mulvaney, Secretary of State Mike Pompeo, former National Security Advisor John Bolton and others - was “in the loop”.

The word “bombshell” gets thrown around a lot these days, but Sondland’s testimony, which represents a shift from his earlier closed-door statements, is a watershed moment in these impeachment investigations.

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Sondland is asked about the call he placed to Trump from a restaurant in Kyiv on his mobile phone.

"I have unclassified conversations all the time from landlines that are unsecured and cell phones," he says when asked if he was concerned about using his own phone in a city that is said to be widely surveilled by Russian security services.

Trump, he says, was also aware that the line was unclassified.

"Did you say [to Trump] 'Zelensky loves your ass'?" asks the Democrat counsel.

"Sounds like something I would say," replies a chuckling Sondland, eliciting rare laughter in the hearing room.

"That's how president Trump and I communicate.

"Lots of four-letter words. In this case three letters."

It's question time.

Each party, in addition to their top members - Schiff for the Democrats and Nunes for the Republicans - also has counsel who will ask questions during the 45 minute period.

US Ambassador to the EU Gordon Sondland describes in his opening statement to Congress how they were made to work with Rudy Giuliani, President Donald Trump's personal lawyer, on Ukraine matters.

Trump's defenders will be pleased by this exchange from the hearing. Sondland says when he directly asked the president what he wanted from Ukraine, he testily denied any ulterior motives.

"I called the president, I believe it was on the 9th of September," the ambassador tells Democratic chairman Schiff.

"What do you want from Ukraine?" he says he asked the US president.

"I keep hearing all these different ideas and theories and this and that. What do you want?"

"And it was a very short, abrupt conversation. He was not in a good mood."

Trump, he said, replied: "'I want nothing. I want nothing. I want no quid pro quo.

"Tell Zelensky to do the right thing."

"Something to that effect."

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Republican Nunes earlier said: "Remind my friends on the other side of the aisle that our first President, George Washington, directed his own diplomatic channels to secure a treaty with Great Britain.

"If my Democratic colleagues were around in 1794, they'd probably want to impeach him, too."

Nunes is referencing the Jay Treaty (formally called the Treaty of Amity Commerce and Navigation).

In 1794, Washington sent Supreme Court Chief Justice John Jay as his special envoy to Great Britain - without congressional approval, according to the Washington Library at Mount Vernon, external.

Though the treaty was seen by outraged hawks as too accommodating to America's former adversary, it was narrowly ratified by Congress in 1795.

Sondland has finished his opening statement now.

The BBC Americas Bureaux Editor Paul Danahar, who is based in Washington, thinks it won't have gone down too well in the White House. He says Trump is probably furious with his ambassador to the EU.

Some important context here - Sondland has a complicated relationship with Trump. He made his wealth in a hotel business in Oregon and Washington states. But he donated to Jeb Bush in the 2016 election campaign, and was occasionally critical of Trump.

However, he switched to the president for his inauguration. He gave $1m to that event.

Democratic chairman Schiff asks about Sondland's claim that he was on a "continuum that got more insidious over time".

Sondland says he left a White House meeting on 23 May, with a "request [that] was very generic for an investigation of corruption in a very vanilla sense and dealing with some of the oligarch problems in Ukraine".

"As time went on, more specific items got added to the menu", including Burisma and alleged Ukraine meddling in the US election, he says.

"It became more and more difficult to secure a [Trump-Zelensky] White House meeting", he says, because more US conditions were continually being placed on Ukraine.

He says an investigation of the Bidens was not a condition he was aware of until later.