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Throughout the impeachment proceedings, a major character in the Trump-Ukraine matter has been getting a lot of attention, including from federal prosecutors: Rudolph W. Giuliani.

Let’s spend a few minutes exploring what’s up with him. Starting with the basics.

Who is Rudy Giuliani?

Trump and Giuliani in 2015 as Trump was running for president. (Seth Wenig/AP)

He was mayor of New York during the Sept. 11, 2001, terrorist attacks. He ran for president in the Republican primary in 2008. He has remade himself into an international consultant and President Trump’s personal lawyer.

What he does for Trump: You might think Giuliani has an official role in the administration, given how prominent he is. But Giuliani is one of Trump’s personal lawyers. Most presidents have those, but we don’t hear from them much. Giuliani, by contrast, talks to the news media a lot about what he does, and he has a seemingly large, if nebulous, portfolio.

He has defended the president during legal scrutiny of Trump’s personal life, such as whether Trump knew about hush payments to women who, during the election, claimed they had had affairs with him. And he helped advise Trump on whether to talk to special counsel Robert S. Mueller III. Giuliani has said he’s working for free for the president. The lines are blurry on what exactly he does for Trump. They’ll get even blurrier when we step back to talk about Giuliani’s other business.

How he’s involved in the impeachment inquiry: He was traveling in Ukraine this year, trying to dig up dirt on former vice president Joe Biden and undermine the finding that Russia interfered in the election for Trump.

Diplomats who testified in the impeachment inquiry said Giuliani was the ringleader of the effort to get Ukraine’s president to agree to announce investigations into Democrats before Volodymyr Zelensky could come to the Oval Office. Two of them said Trump instructed them to “talk to Rudy” when they tried to home in on exactly what Trump wanted Ukraine to do.

Giuliani is mentioned four times in the July 25 call between Trump and Zelensky, by both leaders.

“Rudy very much knows what’s happening, and he is a very capable guy,” Trump said after Zelensky agreed to work with Trump on investigating a conspiracy theory about Ukraine interfering in the 2016 election. “If you could speak to him, that would be great.”

How he could be involved in the actual impeachment and the Senate trial: Democrats have pointed to Giuliani’s work as a reason to impeach Trump, fast. At the height of the impeachment inquiry, Giuliani went to Ukraine and Europe on a supposed fact-finding mission to try to bolster his unproved claims about Democrats. The Washington Post has also reported that he has his hands in diplomacy with a number of other countries — despite not having an official government role.

“This pattern of conduct represents a continuing risk to the country,” House Judiciary Chairman Jerrold E. Nadler (D-N.Y.) said of Giuliani’s travels in an impeachment hearing.

But Giuliani isn’t deterred. He said the president wants him to brief the Justice Department and Senate Republicans on what he claims to have found in his travels. As The Post’s Josh Dawsey reported, it’s not clear if either of them wants to hear from Giuliani. Attorney General William P. Barr has warned Trump that Giuliani is a liability.

Trump doesn’t seem to have listened. “He says he has a lot of good information,” Trump said Saturday about his lawyer. “I hear he has found plenty.”

Giuliani could get even more involved. The Senate trial will allow Trump to have a lawyer defend him. Could he pick Giuliani? It’s not out of the realm of possibility, given how much Trump has embraced Giuliani even in this impeachment inquiry.

Let’s talk about the legal scrutiny he’s under

Giuliani isn’t just Trump’s personal lawyer. He also runs a consulting business, and his list of clients includes people such as a wealthy Venezuelan whose energy company is facing money-laundering charges in the United States. The Post reported that at the same time Giuliani was working with Ukraine’s then-top prosecutor, Yuri Lutsenko, to dig up dirt on Biden and his son Hunter Biden, he was in talks to represent Lutsenko for a hefty sum. Lutsenko has been described by U.S. diplomats as “corrupt.”

At the very least, Giuliani’s work has the appearance of a conflict of interest: He’s helping foreigners dealing with the government while he also represents the president.

In late November, things got much more serious for Giuliani. We learned federal prosecutors are looking into Giuliani’s consulting firm.

The focus of their investigation is two of Giuliani’s business associates with ties to Ukraine, Lev Parnas and Igor Fruman. They were arrested in October and charged with funneling foreign money into U.S. campaigns as they tried to get rid of the U.S. ambassador to Ukraine. (Trump ousted her.)

That criminal investigation has expanded to explore other crimes, such as potential wire fraud, destroying documents and failure to register as a foreign lobbyist, The Post reported. As the inquiry expands, investigators have started looking at Giuliani’s dealings with Parnas and Fruman, including his consulting work for them and donations they made to a main Trump super PAC. The Wall Street Journal has also reported that prosecutors are asking whether Giuliani broke the law by not registering as a foreign lobbyist.

The investigation is actually being conducted by the office Giuliani used to lead, the Southern District of New York. He says, without evidence, that he’s being unfairly targeted because he’s the president’s lawyer.

“I believe that the leaks and the investigation is intended to intimidate me as the president’s lawyer,” Giuliani told The Post’s Dawsey. “I am fully confident that I did not commit any crimes of any kind. They’re going after the wrong guy. The more they try to intimidate me, the more I think, I better go get additional evidence.”

How Giuliani’s legal issues impact impeachment

Lawmakers and staff listen during the impeachment inquiry's public hearings. (Andrew Harrer/Reuters) (Pool/Reuters)

It’s not clear. What federal prosecutors investigate is separate from what Congress investigates.

But it is notable that Giuliani, Parnas and Fruman were central to spreading unproved allegations about Biden, former U.S. ambassador to Ukraine Marie Yovanovitch and Ukraine’s role in the 2016 U.S. election. These allegations made their way to the president and eventually were the genesis of the impeachment inquiry.

Parnas and Fruman have been indicted over their activities, and Giuliani is under intense scrutiny.

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