As I understand it:
1) allegiance gets lower the further you are away from your home planet
2) media centres gradually lower the allegiance of enemy planets
3) Cap ships (for Vasari at least) help to protect against this. (Do they also raise allegiance on unthreatened worlds?)
Do media centres raise allegiance of the planets they are built on? Do they raise allegiance of friendly planets nearby as well (ie should one build them just to help far-off colonies have higher allegiance)?
Will your planets' allegiance gradually rise over time even without media centres nearby as long as they are not near enemy media centres?
How is distance calculated for allegiance purposes - number of jumps from home planet or distance "as the crow flies?" Particularly, how is allegiance affected by being in another star system from your home planet?
Aside from research into greater efficiency of media centres and building more of them (and maybe stationing cap ships over your distant worlds) are there any other ways to fight the culture wars effectively?