No don't get all buddy buddy with everyone fight for every inch of terrain you claim.
Atm as far as I know the following covenants claim dominance over the following areas
Priscilla's Lifehunters- Painted World
Gravesworn- Catacombs and Tomb of the Giants
Protectors of Lord Gwyn- Kiln, Anor Londo, etc
These three at the momment are the most supported groups as I see it.
In time we many see the Servants of Izalith take over the Demon Ruins or Lost Izalith.
Its hard to find a place these days. So ya gotta work hard for it.
@ Successor- I love Jace Belaren, he's my fav plains walker. Shame his abilities never fitteed in with my Dominance themed Blue/Red deck.