On the first day of work at the Consumer Financial Protection Bureau after former director Richard Cordray stepped down, two people showed up to lead the agency: White House budget director Mick Mulvaney, President Trump's appointee for acting director, and the CFPB's deputy director Leandra English, Cordray's pick.

The big picture: The CFPB's General Counsel has said she acknowledges Mulvaney's authority, but it is still unclear who will ultimately lead the agency. Neither Mulvaney nor English have backed down, and both sent introductory emails to staff Monday morning.

Where things stand

On his first day...

Mulvaney showed up to the CFPB with donuts, and then he sent a memo to staffers telling them to "disregard any instructions" from English "in her presumed capacity as acting director."

John Czwartacki, Mulvaney's top communications aide, told Axios that the budget directors transition at the CFPB "could not have been smoother."

On her first day...

English also sent an email to staff, introducing herself and signing off as "Acting Director."

But Czwartacki told Axios he has not seen English, or anyone acting as her proxy, at the agency's office.

English has sued the Trump administration for its appointment of Mulvaney to the post, citing the Dodd-Frank Act.

Monday afternoon, she is scheduled to meet with Sen. Elizabeth Warren on Capitol Hill.

What's next

Per the Dodd-Frank Act of 2008...

The deputy director "shall serve as acting Director in the absence or unavailability of the Director."

Deepak Gupta, English's lawyer, has said she is to serve as acting director until the Senate confirms a new director, per the law.

Sen. Dick Durbin said on CNN's State of the Union that Dodd-Frank "says that when the director steps aside, the deputy director shall be in charge of the agency ... Not may — shall — be in charge."

Per the Vacancies Reform Act of 1998...