My question related to exploited systems is:
Why some squadrons/players involved in powerplay want to put exploited systems under the control of their powerplay major faction (imp/fed)?
For example, I have come across Arissa Lavigny supporters asking me not to gain influence for independent minor factions in exploited systems controlled by imperial factions.
Is that just role play?
I don't see how a controlling minor faction in an exploited system affects the amount of CC received.
Powers prepare and then expand into a system that becomes controlled.
All populated systems within 15 ly of that system become "exploited" - making it a sphere. If there are already exploited systems from other powers, those become "contested" instead (and the governments there won't matter at all for PP) and neither of the involved powers get the CC for those systems.
Every power has a few government types they are "strong" or "weak" against, which you can check at Power_Name -> Control -> Overview (yes, that's a button you can click on). For Arissa:
This means that in Arissa exploited systems it will be better for her to have feudal and patronage minor factions in charge of the systems. The superpower of the factions do not matter at all for PP.
Once a control sphere has the majority of its exploited systems with a "strong" government-type, the effort it takes for players to fortify the control system of that sphere is reduced by half. So far example, if the trigger is 5000, it will be reduced to 2500 - making it much faster (and cheaper). Succesful fortification of a system removes the CC upkeep cost for the next cycle, or cancels out with the undermine trigger if both are reached. Undermined systems that haven't been fortified will instead lose all that sphere's CC income for the next cycle.