Do specify the zone, maybe everyone has its own rule. but the point is (to logger):
>What is the procedure to transfer a domain to another Registrar? I must ask the current Registrar to have changed >admin-c handle on my nick and after that registrars understand each other?
\r
registrars to understand each other WILL not. you have tech Registrar's request so-called auth code (transfer code) then the new transfer domain, where enter this code, but then they have as you say "agree among themselves", although it all happens automatically
\r
PS: and still call the area, maybe in the TLD — one rules (much more transparent, simpler and more correct), and in local areas their own, where everything is much more complicated