I don't know how he handled it but in Arizona, in a private sale, it's up to the buyer to take care of the registration, license plates and insurance. Speaking of the license plate, in Arizona, the seller gets to keep that and it is up to the buyer to have a "temporary plate" to put on the vehicle to get it home.
I can say there is something that the seller must be sure to do.
On his registration slip, he needs to write the name and address of the buyer on the back and then mail it to the Arizona Department of Motor Vehicle's to let them know the vehicle was sold.
I knew a guy who didn't think about this so he gave the registration paper to the buyer.
The buyer didn't bother register the vehicle to get a title. Instead, he parked the car anywhere he wanted to for as long as he wanted. That resulted in dozens of unpaid parking tickets, all in the sellers name. He had a hell of a time trying to convince the DMV and the courts that he didn't own it any longer and it ended up costing him a lot of money.