I tell people that if they want to keep their plates, they have two choices if I’m buying the car.... Either they deliver the car to my place, or they pay for the rollback to get it there, on their dime. Haven’t had anyone want to keep the plates yet.
As to the paperwork, it’s all filled out and signed, and they get a copy of it all before I leave. I usually hit the tax office within 24 hours, to do the title change.
Only had questions on one car we sold. Got contacted by the cops when they confiscated a Porsche we sold. Told them it had been sold about 5 years earlier. Could have retreived it if I wanted to, but it was torn up bad at that point.