On my Mac OS 10.5.8 I've deleted iTunes (by dragging it from Applications to trash and then emptying the bin. However, approximately once a week Mac OS suggests installing an update for it. Why and how to stop it?
When in the software update application select the iTunes update that is being offered to you and press delete (keyboard) or go to the update menu in the toolbar and select 'Ignore this update'.
Try deleting the application (and its hidden Package Contents) with an uninstaller for Mac. I suggest AppCleaner
It sounds like you did not completely remove iTunes when you deleted it.