As for territorial disputes...
alot (not all or not all the time) is sound and fury, dominance displays if you like. If one doesn't back down, then it gets a bit hairy and there is spitting and talons etc. And yes some disputes are to the death. They are also gender specific - females fight females, males fight males.
I have always read that territorial battles are gender specific, but it seems that at the Brighton, England nest yesterday there was a territorial battle between the resident female and a new male (who was actually born at that nest two years ago). There have already been changes at the nest this year - last year's unbanded male did not return, and a new banded male from Chichester, born 2005, moved in.
TPC, I'd be very interested in your comments on this battle - it seems unusual for a female and a male to fight. There is a video on the Diary page of the site:
http://www.regencybrighton.com/birds/
Fights between females & males are territorial, its one bird driving off an unwanted suitor. Last year, Ivy hung out at the Radisson and Princess (his Mom) didn't drive him off but wouldn't go anywhere near him or let him anywhere near her. When Trey arrived, Ivy beat a hasty retreat and exited the territory before there was a problem (smart kid). Because males are smaller than females, they tend to avoid antagonistic situations with them - also, for a male to attack a female or vice versa is counter-productive from a genetic perspective, you may be evicting/injuring/killing a potential mate. Driving off an unwanted suitor is something else however ...
From the video, I suspect that the new male got himself into trouble by entering the nestbox when the resident female was there, no way she would give it up, regardless of the gender of the intruder. I'm surprised that such an experienced male would put himself at risk like that ... and that was a true knock-down-drag-out fight, surprised everyone (so far) has survived. Hopefully he won't be back ...