Not all of media baron Rupert Murdoch’s kids want a piece of the family business.

Elisabeth Murdoch turned down a spot on dad’s News Corporation board, Fortune reports. She was simply an "observer" at today’s board meeting — the first since President Peter Chernin announced that he was leaving. "Liz" rejection further adds fuel to the debate over who will take the company’s reins once the elder Murdoch steps aside.

It’s no secret ole Rupert wants control kept in the family; he has four adult children who could easily take over. Other than Liz, there’s Lachlan, 37, James, 36, and Prue, an elder daughter he had with his first wife — and whom Vanity Fair’s Michael Wolff recently characterized as the "official Murdoch family wing nut." Prue isn’t involved in the business, but her husband is a ranking company executive. Murdoch also has two very young daughters with current wife Wendi Deng. It’s believed that James, who runs the European and Asian arms of the businesses from London, will most likely be the successor, in spite of his critics.

Liz — now married to Matthew Freud, great grandson of Sigmund Freud — has had a rocky relationship with her father. She left Australia’s News Corp branch not long after she married her former hubby in 1993, but eventually became an executive at News Corp satellite TV provider BSkyB. But, after some disputes with other management, she left in 2000, forming Shine a year later.

Vanity Fair chronicles how she was a "harridan of a manager — ripping through the staff, sacking many old stalwarts and slashing operating costs" during one of her early ventures. Dad also reportedly wasn’t very approving of the way she went about her marriage and her child-bearing schedule. That said, her reluctance to return to the fold shouldn’t come as much of a surprise. This doesn’t mean Liz will never return to the company. She told The New York Times last year that she could, but doesn’t have a timetable: "I don’t know how it would happen one day, but it’s certainly not out of the cards.”

If she does come back, don’t expect her to do it quietly. In 2007, Liz was named the world’s most "powerful blonde" by Tatler magazine, beating Prince Harry’s girlfriend Chelsy Davy, along with women like Camilla Parker Bowles and Sienna Miller.