...
Either before or during the Op (via Behaviour), the target needs to be nullified (taking out the engines, turrets and shields; reducing crew levels through hull damage). To initiate boarding, select the desired player-owned ship(s) and then right click the target and order Marines to Board the target.
...
Administrative Centre modules, when completed at a player station, grant ownership of an unowned sector on a first come first served basis, revealing all ships and stations in the sector and imposing the illegal wares list of the owning faction.
If the Administrative Centre module is destroyed, sector ownership will change over to the next faction with an Administrative Centre. Warring NPC factions are constantly playing a turf war to replace the Defence Platforms of their enemy with one of their own. Once the player has acquired Blueprints for an Administrative Centre, they too can conquer entire sectors if they are willing to defend it.
If a faction is about to challenge you for the ownership then there will be a warning "(Contested)" behind the name of your system indicating a construction of a station with an admin module has commenced.