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That is, do you get additional benefits for having more than one Broadcast Center in your gravity well?
Thanks.
indeed you do. and its something that actually happens in some situations, for example to attack or defend culturally near borders. I am not sure, but I think there is a cap to it, so it does not rise indefinately.
tbh I do not put a huge emphasis on culture, unless pressed into it. I try to get the tech along the way and spread a few around my empire, so that every planet gets it at least from its neighbouring planet which is enough to raise the allegiance cap for the extra resources. only if I see an opportunity or a threat do I concentrate them more.
but then I do not consider myself a pro, so consider that.
Yes and no.
Culture spread from broadcast centers is cumulative, so it will spread faster if you have more than one. Besides that, it also factors into combatting hostile culture if it meets - whoever spreads at the highest rate will win eventually, how fast that happens depends on the difference in rates (for example, if you generate 12/second from a planet and the neighboring enemy planet generates 10/second, you'll win but yours only spreads at 2/second towards the enemy planet and it will take a while. If you're generating 20/second, you'll get a 10/second spread after the enemy culture is neutralized).
The "no" part is with the secondary effect of culture - allegiance gain/loss. This rate is capped, so shoving tons of culture down an enemy planet will beat back their culture faster, but it won't cause the planet to rebel any faster.
This combines into a general rule of thumb I follow: to make sure I have my inside territory covered by culture, I build 1 broadcast center for every few planets, since culture spread diminishes with each jump. For front-line worlds I build more, since the goal is to battle enemy culture in many cases.
The only real limit is how many logistics slots you have on your planet and the number of phase lanes to that gravity well. Desert planets can be choked with 9 broadcast centres (10 if you're TEC and have Development Mandate researched) if you use all the logistics slots for them. Planets with fewer phase lanes have faster spread down those lanes.
Culture, however, apparently also has a resistance to being pushed back by hostile culture (Manifest Dominion gives a 10% bonus to resistance to hostile culture, Advent culture tech Wall of Faith can increase resistance by up to 40%), though I don't know how that plays out.
Im in the habit of placing 1 broadcast center on all of my planets. Crazy?
No, usually I have 1-2 on each planet depending on which player has the most control of a system. Against the AI I usually put one on each planet and then at planets with lots of Phase lands 2-3.
It's very crazy. Too many broadcast centers will eventually cause your own population to rebel against you, after having to watch the same washed out reality shows non-stop 24/7. Shows such as "The Slave", where contestants compete to be enslaved by a charming Vasari overlord with "eliminations" being quite literal, and "Who Wants To Be a Ship Captain", where contestants compete for a spot commanding a military vessel, to boost the military's need for fresh rookies to send on suicide missions. That's not even mentioning the rather depressing "Where Are They Now" segments for these shows 
No, you're not crazy.
An enemy can't usually colonize a planet still under your culture. If your culture is still in effect over several phase jumps, they can't 'take' your planets. You end up denying them the resoruces and staging points they'd otherwise have. This is where the advent super-weapon begins to shine...
I don't build broacast centers at the expense of my fleets, but I do try to have a few by mid-game, and on all my frontier planets from that point forward.
Culture spread is reduced when going through planets. TEC has a tech that allows that reduction to be less. Advent just have lots of culture increases and a superweapon which flings a big blob o' culture at a planet. Vasari have SFA
one culture structure every few systems is fine for the back lines. Your 'front line' generally needs a few culture centres per planet (if you plan for it to be your front line for a long time). Having your capital nearby seems to help with culture spread. Advent superweapon wrecks anyone's culture day but their own.
As Vasari. You get salvage for blowing up orbital structures and cap ships... kill things already. Wipe out nearby systems, EVEN if you can't hold them. Raid, raid, raid. Their culture spread diminishes as it passes planets too.
As TEC, a wall, one or two systems thick at the edge of your empire should push your culture fairly deep into their space if it has enough broadcast centres.
As Advent. I KNOW people say the superweapons are expensive, but if you're fighting a culture war, it takes less resources to win it with deliverance engines AND culture structures than culture structures alone. If you have Deliverence engines, you don't NEED to win the culture war, just ... don't lose it and drop a deliverance hit on any system you want to fight in, colonize, or otherwise win at culture. Have a couple of backups for sustained ops. They are also priceless for giving a new homeworld a big boost in loyalty FASTER than loyalty drops at the old site, meaning you will get back the resources used to move it by having 2 areas of elevated loyalty.
I play TEC and just put one at every planet once i have the resources but i tend to put more on refinerys and trade ports than culture as long as none of my planets have enamy culture touching them it's fine. then hopefull my cap ships on the raids/colinzing a new planet keeps it down i have never had a problem with it really.
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