Are Battlegrounds Cross Realm?

Battlegrounds are cross-realm, which means you'll fight alongside allies and against opponents from all of the realms in your region.

Are wow classic battlegrounds cross server?

Yes, they are cross realm.

Is rated PvP cross realm wow?

Players can queue for arenas through the PvP interface. ... For rated mode, players in a party of the appropriate size (cross-realm groups are supported) may queue for an arena bracket of the same size.