In 2 games I build a United Planets Headquarters. In both cases my influance was boosted to cover almost the entire map (from a 20% coverage)... Nothing else was build that turn..
Also, in the second game I destroyed all the improvements on the colony the United Planets Headquarters was build on (no other way to get rid of it ?) and after that the influance was reduced to "normal".
On a related note, is there anothrer way to destroy special buildings? As destroying the colony does not give the option to rebuild a starbase..
