Judicial branch claims to be independent. It picks the judge. Venue is established by other rules, generally being the location of the crime or location of an actor.
Executive branch has no say, other than it can argue for recusal.
Does the Chief Justice not preside? Chief Justice William Rehnquist presided over Clinton. But I've heard (can't remember the reason) that perhaps Roberts would have to recuse.
“Executive branch has no say, other than it can argue for recusal.”
I LOVE IT WHEN YOU POP UP. :)