“Mr. Trump and Mr. Cohen have a lot of explaining to do.”

They’re not the only ones.

Tweeting those words Tuesday evening, lawyer Michael Avenatti touched off a scramble in companies from South Korea to Switzerland to explain how they came to deposit money in the account of Donald Trump’s lawyer and longtime fixer, Michael Cohen.

The self-styled dossier released by Avenatti, who represents porn actress Stormy Daniels in litigation against Trump, introduced wide-ranging allegations of suspicious transactions running through an account that Cohen opened just before the 2016 presidential election. Besides offering a potential new view on links between Russia and Trump, it brings scrutiny to global companies AT&T, Novartis and Korea Aerospace Industries.

Those companies acknowledged late Tuesday that they’d made payments to an account for Cohen’s Essential Consultants, a Delaware-registered shell company, saying they were for legitimate services ranging from real estate consulting to “insights” into White House policy.

A company linked to Russian oligarch Viktor Vekselberg, among a handful of Russians since sanctioned by the U.S. over the Kremlin’s election meddling, hasn’t denied making $500,000 in deposits into the Cohen account. But the U.S. company, Columbus Nova, and Vekselberg deny the money had anything to do with him.

“The ‘explanations’ being provided by these various entities are raising many more additional questions than they are answering,” Avenatti said by telephone Wednesday, saying Cohen should disclose who paid him and why. “Unfortunately, I am just a lawyer. Michael Cohen evidently is a lawyer, a real estate agent, an accountant, a doctor, a business consultant and a venture capitalist. Who knew that Michael Cohen would be exposed as the Leonardo da Vinci of our time?”

Among the questions: How were these companies steered toward Cohen’s limited-liability company, the sort of entity designed to obscure its ownership? Where did money that hit the Cohen account – more than $4 million, by Avenatti’s count – go from there? Are there other such companies?

Without a more complete view, there’s no telling whether such payments crossed legal lines. Providing political intelligence isn’t illegal. Even if Cohen did any lobbying – AT&T and others said he didn’t – he generally would have had to register only if that work took up more than one-fifth of his time for the client.

Federal prosecutors in Manhattan are investigating potential bank fraud and other matters connected to Cohen’s business following a referral from Special Counsel Robert Mueller’s office, but they haven’t leveled any allegations.

Avenatti, in an interview Tuesday night with MSNBC’s Lawrence O’Donnell, said First Republic Bank, where Cohen held the account, flagged some of the transactions to the U.S. Treasury via so-called suspicious activity reports. He called on Treasury Secretary Steven Mnuchin to make those reports public.

The timing and circumstances of the payments from a company linked to a now-sanctioned Russian oligarch to the president’s longtime fixer also raise serious questions about whether it was a payment in exchange for something that Trump did or promised to do to benefit the Russians, said Mimi Rocah, a former federal prosecutor in New York.

“We don’t know the answer to that very important question yet but one thing is for sure – investigators in U.S. attorney’s office in Manhattan and the special counsel have probably been digging into that already for some time and will try to get to the bottom of it,” Rocah said.

Payments from companies, ostensibly for consulting, could merit similar scrutiny, Rocah said. “Was it paying for something else? It’s harder with American companies because the law is very narrow in terms of what constitutes a bribe. You can pay money to get access to politics and curry favor – you just can’t pay money to get an official action,” she said.

Novartis said it entered into a one-year agreement with Essential Consultants in February 2017, focused on U.S. health care matters.

“The engagement of Essential Consultants predated Vas Narasimhan becoming Novartis CEO. Dr. Narasimhan had no involvement whatsoever with this arrangement,” the company said in a statement. Novartis said it was contacted by Mueller’s office in November 2017 regarding the consulting agreement and that it cooperated fully and considers the matter closed.

AT&T didn’t immediately respond to additional questions about the payments on Wednesday. “They did no legal or lobbying work for us, and the contract ended in December 2017,” AT&T previously said.

Bloomberg’s Jared S. Hopkins contributed to this story.