Our cats fight over the kitty beds, too. Now we have a comforter folded up at the end of the bed and there's room for both of them. The larger one doesn't know what to make of this. He keeps feeling he ought to be trying to get what the smaller one is getting, i.e., her spot, but there's no boundary for him to use to assert this.
You folks who actually
have desks
and places to keep them... I have a rolling cart that I can use in the bedroom or on the couch or in the dining room. No desk, no office, no private space.
(The bedroom comes closest to "private space," until the Muffin Man wants to sleep, at which time I move out to another room.)