I made an antipope myself, it didn't seem to do much, then he died and was succeeded by a guy with a bunch of religious traits, like zealous, celibate etc... My income jumped from 11 gold per month, to 16 gold per month.
Then the pope died, and was succeeded by a guy with a bunch of unreligious traits. My income then jumped to 27 gold per month... I'm loving my antipope, I just wish he wouldn't keep excommunicating my chosen successor on behalf of my eldest son. It's really draining my piety to keep lifting the excommunication. Yeah, and I don't know how you actually lose an antipope either.
Elective monarchies are also awesome. It gives you a boost with your vassals, although not vassals that are related to you, which can make appointing sons with land rather awkward. It's also really easy to control who gets the succession, especially when there are only two votes, and you have one of those votes, and the duke you appointed as successor has the other vote. Then when you succeed and the duke you become that duke, you then gift your old lands to a new successor. It guarantees the loyalty of someone whom you can invest with quite a lot of land.
This democratic process is streamlined in my crown of Finnland, where there is a one man, one vote, system. I am the man, and I get the vote. It's the perfect democracy... at least until another duchy is created.