[Daynarr]

Well, you can't tell who owns the system in the map in the main windows, unless you have some ships (or satellites) there. You can use Empires screen (F9), and then look at borders. There you will see all the systems you have discovered so far, and also all the claims on those systems. Now, when the AI colonizes some system, he always puts claim on that system and all the neigboring systems. Because of that, you can easily predict where AI empire has colonies.