depends. Normally the registrar also is the DNS server provider. Having them at different places means normally you run your own, but I guess you do not do that?
So for a normal handover the new registrar would just take over the values currently in the DNS and move everything to their own infrastructure.
Takes a while until it is reflected everywhere.
Edit: Special setup you have done needs to be renewed most of the times though. And I also have experience in between 3 so far