iTunes keeps opening itself

Whenever the computer is on (iMac 2GHz, OSX 10.4.11) iTunes keeps opening itself. Never did this before but recently ( a couple weeks ago) I allowed an auto software update, that's about the only change I can think of, but it only started doing this a couple days ago. I close the application and within a couple minutes it has opened itself again, underneath whatever application I happen to be using (close that app and there is iTunes, opened again lurking under the app window I was looking at). It does this over and over, even when the computer is in sleep mode.

Help?