Capturing Worlds and Fleets
The rules for ownership of worlds and fleets are fundamentally simple: you will automatically capture any world or fleet when you are the only player with ships there.
That is to say, if you bring a fleet to a world, and there is no other player with fleets at that world, and there are no D-Ships on that world, then you will become the new owner of the world, as well as of any (empty) fleet keys at that world.
On the other hand, if two different players bring their fleets to a world at the same time, then ownership of the world does not change. If the world was previously owned by anyone, it will remain owned by that player. If the world was previously neutral, it will remain neutral. If there are any empty fleet keys at the world, they will become neutral (even if they were previously owned by a player).
Note that if you have any empty fleet keys at a world, you will lose ownership of them if another player brings a fleet there. At the best, they will become neutral; and at the worst, they will be owned by the newcomer. If you want to keep ownership of your fleet keys, it is best to keep at least one ship on each one.