One could argue that Paula simply wasn't offered an upgraded contract by Fox, but her reps are saying she "quit" so we'll give her that. It's the least we can do considering she went the same way as Sharon Osbourne - put out to pasture by a younger model drafted in by Simon Cowell (Kara DioGuardi signed her new contract last Tuesday).
Abdul released something resembling a statement, saying: "With sadness in my heart, I've decided not to return... I'll miss nurturing all the new talent but, most of all, being a part of a show that I helped from day one become an international phenomenon (not bitter). What I want to say most is how much I appreciate the undying support and enormous love that you have showered upon me."
The Fawx Network, meanwhile, said: "While Paula will not be continuing with us, she's a tremendous talent and we wish her the best."
According to BBC News: "In an interview last month, Abdul said she had been invited to stay with the show as long as it aired and that she was optimistic about negotiating a new contract."