Relays generally dont rebroadcast, there are some blastr relays that send every note to a list of the top relays. But network synchronization isnt presently in the protocol. Relays were intentionally designed to be dumb for resiliency.
Discussion
I meant rebroadcast as in if a user rebroadcast a particular note (there's a button for it on amythest).
A blastr relay is slightly different as that connects relay to relay. You are right that typically relay connect peer1>relay1>peer2.
In my example, when I say broadcast, I mean if peer2 broadcasts my note to relay2 which I'm not connected to.