Confirming here that at the end of EpIII, 3PO and R2 are put into the custody of Antilles.

The Emperor sees Vader as his apprentice. Because Vader took so much damage, he can never usurp the Emperor in typical Sith fashion. So that makes Vader the perfect henchman... and in Sith fashion the Emperor has to constantly test Vader and keep him on his toes (reminding Vader he’s missing those)