I think there was something in here about culture for stars.
Culture itself only spreads through phase lanes and does not go between stars. On the other hand, just playing old Allegience does. For allegience, the jump between stars just counts as one phase jump, so you suffer the same ill efects as if it was in your own star system.
A planet 3 jumps away from your capital = 70% allegience, while a plant one jump from a star (with your capital being 1 jump from another star, too) also = 70%
*This is just an illustration and the percentages are not correct. Please do not attack me for this.
Also, although stars can be great check points, keep in mind that since the are much larger than planets (and since you can't make tactical structurs around them), you need a lot more ships to keep them secure.