Broadcast towers do help your planets, both by repelling enemy culture (which lowers allegiance), and by raising it. The cap is 10% higher then what the planet starts at, so your capital can actually go to 110% (120% for Advent).

Otherwise it's as Annatar said. The maximum is figured out based on the total jumps between the world and your capital. For really big maps, far off worlds will cap at 35%, and nothing can raise it except the Advent tech.

One trick is if the map has a lot of stars, move your capital to a world that connects directly to the star. The star counts as a jump, but since the star connects to all other stars directly, it really helps planets in other systems. If your capital is 3 hops from the star, any planet in another system is going to be pretty crippled resource wise.

The only stackable effect of broadcast stations is the rate of culture spread. Simply put, 2 broadcast stations have 2x the culture output of one station.

Well, the rate of culture spread drops off with each jump. The more culture you output, the more is left after a jump so it can go longer before it slows to an unnoticeable crawl

No, rate isn't distance, but they're related! Let's take some random numbers. One broadcast center produces something like 5 culture/sec. Let's say to make it easy that each jump halves the culture rate.

If you have 1 building, you have 5/s to the next planet. Then 2.5/s, then 1.25/s, and .625/s and you probably stop noticing it moving after that. So it's probably good for 3 jumps or so, though even 1.25/s is pretty slow crawling.

Now you have 4 buildings, so you have 20/s to the next planet. Then 10/s, 5/s, 2.5/s, 1.25/s, .625/s and so on. So now it spreads decently fast for a few more jumps, before it starts crawling.

Note that half is just what I used for easy math, I'm not sure on the actual reduction.

Ah ha! I geddit! You da man! I gotta try and counting some of this stacking effect next.. I usually just add on one broadcast center every other jump or so.. But clearly, the strat should be to load up on broadcast centers at key intersections to help boost signal strength.. Damn, running out of logistics slots at these key intersections.. crap..