Several sources mention the "treaty exploration zone". Combined with the Prime Directive (Reeves-Stevens') idea of trust worlds, I'm thinking the early UFP claimed a huge swath of space to set aside those trust worlds. The idea is that, when a world gets into space, worlds are set aside for them to colonize. In the novel, Talin IV had 48 worlds in a 25 parsec radius set aside for them. As mentioned above, the Organian treaty kinda supersedes that in at least quadrant 2, since the Klingons and UFP have to show who can develop a world better.
They were probably unduly optimistic when they founded the UFP, and nationalistic pride forbids them admitting later they couldn't actually maintain their claim, so there's a lot of nominally
federation space that's not really controlled.
Keep the ideas coming.