In reply to bobtheclimber:
Commonly you do leave some sort of anchor at the top. Smetimes there are bolts or a stake. Sometimes you can thread/sling something. Sometimes you have to leave some gear.
Then there are times you can simply loop your rope around a tree, rock spike etc and ab off that then pull the rope. There are also places where you can counterbalance abseil off a feature, one climber goes down each side of say a fin or spire. Much care is needed to do it safely and there are countless variations on the theme
Sometimes you can downclimb/traverse a little to a feature you can ab off safely and easily (eg tree).
jk