There seems to be some rough edges in gameplay when you "conquer" a competing civilization and make a deal to take ownership of their fleets.
When the other civilizations are failing or have lost all of their planets I have used the diplomacy window to make an offer on their fleets, shipyards and starbases. (slap some new paint on them things and put them on the used space-ship lot).
For ships in space it works out, you just take them over.
For ships that may be in orbit around a planet that you took over a long time ago they will not follow your command to come out of orbit from the planet. On the planetary panel where you see the ships in orbit you cannot do anything to or with them. You almost need to do weird things to the ships before they finally pop-out and then you still cannot control them, I ended up just shooting them down.
For starbases you cannot control them. What I have tried was to send a constructor to them and that seems to convert them over (their color even changes).
Under the diplomacy window there is not even an option for dealing with shipyards. The only choice I have there is to destroy them.
I have noticed that if a civilization goes away that they will sometimes convert to "pirate". You cannot negotiate with pirates, only destroy them... yet they do not do anything to you.
I suggest cleaning up the custodianship transfer of ships, starbases or shipyards to take over or buy.
Secondly I think that the entire "pirates" thing has some opportunity for games expansion. What I suggest is that if you leave pirates in place, that they can attack and pillage undefended planets, starbases or shipyards.
Pirates:
If they get momentary custody of a planet allow them to loot some of the money from the treasury or steal population or techs. Also if they are allowed to stay within a certain distance of your planet allow them to negatively influence the morale and approval ratings of your planet
If they get momentary custody of a starbases allow them to "use it against you" until you take it back
If they get momentary custody of a shipyard allow them to repair or upgrade their ships (using your resources) until you take it back
Game-play would be very similar to how the Vikings used to raid the coastlines off of europe a thousand years ago. The result is if that you engage in war that there can be very unpleasant things that spring up from the wreckage (like weeds).