Update, Sept. 24, 1:39 p.m.: Despite earlier media reports that Deputy Attorney General Rod Rosenstein was willing to resign or was expecting to be fired, he appears to be staying in the job for the time being, and will meet with President Trump on Thursday.

On Friday, the New York Times reported that Deputy Attorney General Rod Rosenstein, the man who oversees Robert Mueller’s special counsel investigation, brought up the idea of “secretly recording” President Donald Trump last year and discussed invoking the 25th Amendment process for removing the president from office.

Rosenstein denied the Times story, calling it “inaccurate and factually incorrect.” Another source or sources have been telling reporters that Rosenstein was joking when he talked about wearing a wire. (The Times has stood by its reporting.)

Trump supporters and right-wing media personalities reacted quickly to the report by calling for Rosenstein’s firing. As with James Comey’s firing last year, the aftermath of Trump removing Rosenstein would be chaotic. The reports Friday raised questions about what would happen at the Department of Justice and with the Mueller investigation if Trump were to make the move.

Who would replace Rosenstein overseeing the Mueller investigation?

Normally, the associate attorney general would step in. But Rachel Brand stepped down from the role in February, leaving the office with a temporary replacement. The most likely answer is that the chain of command would leap over her vacant position and Solicitor General Noel Francisco would take Rosenstein’s place.

What do we know about Francisco?

Like many prominent members of the Trump administration, he has had his share of controversy. Most notably, Francisco has been accused of making misleading arguments before the Supreme Court about Trump’s travel ban.

But before joining the administration, he was more controversial for his legal work on behalf of conservative causes. He often represented corporations in their fights against regulations, including a coal company involved in a deadly mining disaster. And he argued two prominent cases before the Supreme Court, including a defense of religious organizations’ right to deny employees access to birth control.

He also had worked on George W. Bush’s 2000 Florida recount, and then for Bush’s administration as associate counsel to the president and deputy assistant attorney general in the Office of Legal Counsel.

As Jed Shugerman wrote for Slate, Francisco’s background is more political than other career DOJ officials. Mark Joseph Stern called Francisco “competent and qualified” in his assessment in Slate but warned that Francisco displayed some worrying beliefs, including a strong stance on the scope of executive privilege. There’s good reason to believe that if Francisco were to take over Rosenstein’s position, he would be less kind to the Mueller investigation.

Are there any other possible replacements?

Yes. While Francisco would be the natural person to step in per the chain of command, it’s possible Trump could choose instead to replace him with an administration official already confirmed by the Senate under the Vacancies Reform Act of 1998. Louis Seidman, a constitutional law professor at Georgetown University, told the Washington Post that hypothetically Trump could choose someone like Energy Secretary Rick Perry to fill the role. But, Seidman cautioned, it’s not clear whether the act applies to people who have been fired, rather than someone who resigns or dies in office.

The danger for Trump in choosing this route, Shugerman wrote, is that it would be “such a transparent effort to subvert the rule of law as to be a political liability even within the Republican Party.”

How do we then get a new, permanent deputy attorney general?

Trump will eventually nominate a replacement, and that nominee will have to go through the normal Senate confirmation process.

What exactly is Rosenstein’s role with the Russia investigation anyway?

Rosenstein is, effectively, Robert Mueller’s boss. The task of overseeing the investigation would normally have gone to Jeff Sessions, but in March 2017, after it was revealed the attorney general had failed to disclose conversations with the Russian ambassador, Sessions chose to recuse himself from the investigation, infuriating Trump, who saw the decision as a betrayal.

While Mueller does not have to report to Rosenstein for all regular decisions, he does on occasion have to check in with Rosenstein on the status of the investigation. Rosenstein, then, can make Mueller provide explanations for any of his actions and prevent any steps he considers “inappropriate or unwarranted,” as Yale lecturer and former FBI agent Asha Rangappa wrote in Slate last year.

Rosenstein is also responsible for representing the investigation before Congress. Rosenstein has largely acted as a champion of the investigation and has not challenged Mueller’s approach or tactics in any significant ways.

What would his firing mean for the investigation?

There’s room for debate as to how much damage this could actually do. If the person who steps into Rosenstein’s position feels less charitable toward the investigation, that person can throw up significant roadblocks and even, possibly, shut it down.

As Rangappa noted, the investigation by this point is broad, complex, and to a certain degree decentralized. It will almost certainly carry on regardless of who oversees it, as the FBI is compelled to pursue the leads it has and would have to defend any decision to drop specific lines of investigation. The Russia investigation, therefore, could not simply be killed.

So the investigation is safe?

Mostly, but a particularly hostile overseer of the investigation could hobble it by forcing Mueller to justify every step. Rosenstein’s replacement could override one of Mueller’s decisions—but then the replacement, in turn, would have to justify the override to Congress, with reports for both the Senate and House Judiciary Committees. An unethical acting attorney general working against the investigation could also potentially leak Mueller’s plans to the White House in advance.

Possibly the worst threat to the investigation could come from the acting attorney general’s role speaking for the investigation. An acting attorney general keen on discrediting the investigation could, in testifying before Congress, convey a lack of faith in Mueller. That could turn Mueller’s remaining Republican allies in Congress.