“It is highly doubtful that the president will appoint anyone who offered the slightest reservation about taking over for [Rosenstein] in the Mueller investigation,” said former federal prosecutor Jeffrey Cramer. “It seems like that is the first criteria for this White House.”

Whoever replaces Sessions — either in an acting or full-time capacity — the big questions at that point would be whether that person would undo what Rosenstein has done, restrict Mueller’s authorities in some new way, or even retract Mueller’s appointment. Absent those clearly controversial potential moves, it would really be about other new Mueller authorities, charges and immunity deals that may come about. (Mueller doesn’t appear to think he can indict a sitting president.)

Another interesting subplot is whether the new attorney general or acting attorney general might also insert themselves in the Cohen probe, in which the former Trump attorney has just implicated the president in campaign-finance violations over hush-money payments. But SDNY has historically been very independent of the main Justice Department, and that would lead an internal clash, according to experts.