Paula Abdul made her first public, non-Twitter comments since announcing she was leaving the American Idol judge’s table, telling a pack of TMZ photographers at New York’s JFK Airport, “It’s been overwhelming, what’s going on right now, so I have to really carefully think about everything.” TMZ pressed Abdul on whether she had been invited to join former Idol producer Nigel Lythgoe on So You Think You Can Dance, but Abdul reiterated that she doesn’t know yet what her post-Idol future holds. (Though Abdul jokes that she may take up President Barack Obama on his offer to babysit his children.)

While Abdul isn’t sure about her next steps, American Idol is certain they’ll replace her — and the search for a new fourth judge is underway. According to the New York Times’ ArtsBeat blog, Peter Rice, the chairman for entertainment at Fox Broadcasting, told a meeting of the Television Critics Association, “What we need to find is someone who has great chemistry.” During auditions, Katy Perry and Victoria Beckham will sit in as guest judges, and the plan is to fill the fourth chair with a female pop star during the try-outs. Rice said the show hopes to lock down Abdul’s replacement by the time the show begins its regular live broadcasts in January.

Abdul promises to keep in touch with her former castmates, saying judge Simon Cowell — her frequent sparring partner — “misses me already.” When asked what she’ll miss most about leaving AI, Abdul told TMZ, “My compadres, of course, but also, I love the kids. That’s been the joy for me.”

As Rock Daily reported yesterday, both Ryan Seacreat and Randy Jackson were “shocked” and “stunned” when Paula revealed that she would not be joining them for the series’ ninth season. In the end, Abdul and the Idol producers couldn’t come to terms on a new contract; Abdul wanted a deal that was more in line with the massive deal Seacrest just signed and Cowell is poised to sign when his deal expires after this season, while the producers reportedly countered with a multiyear contract with a 30 percent raise over Abdul’s salary. Even though Abdul’s manager previously said it was unlikely Abdul would return, Paula’s announcement yesterday still came as a shock to most fans.

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• Seacrest “Stunned,” Jackson “Shocked” By Abdul’s “Idol” Exit
• Paula Abdul Announces She’s Leaving “American Idol”
• Paula Abdul’s Return to “American Idol” Unlikely, Manager Says