There's no strictly defined ZOI in Disco, yet it can be against the rules to do certain things out of your ZOI (for instance a Corsair pirating in Liberty) and it can in other cases have RP repercussions (for instance an Outcast pirating in Liberty). It's confusing - also for players that's been here for years and years. Your best bet would be to flip through the Laws of Sirius, the wiki for various maps and information on factions and ID's, as well as the various faction subforums.
BHG caps are limited by the associated BHG Core ID which doesn't allow BHG capital ships in any systems with a jumpgate. You are basically limited to the Omegas and the Omicrons.
