According to a number of reports, Rupert Murdoch will step down as CEO of 21st Century Fox—which was split off from the original News Corp. holding company as a separate public entity in 2013—and will hand the reins over to one of his sons, 42-year-old James. The elder Murdoch will apparently stay on as co-executive chairman, a role he will share with his other son Lachlan, 43.

Whether James can handle the job of CEO remains to be seen, however. The only major role he has held single-handedly so far—as opposed to being co-chief operating officer of Fox, the position he holds at the moment, where he shares power with COO Chase Carey—was running News Corp.’s British holdings during the phone-hacking scandal, where his performance was seen as decidedly mixed.

Fox shares tumbled on the news that he is set to take the top spot, although they later recovered somewhat. The company’s share price has been more or less flat since the split that created News Corp. and Fox in 2013.

The fact that Murdoch senior would eventually hand over his power has never been in doubt, of course. The legendary media mogul is 84 years old, and while he is apparently still as feisty and combative as ever—and regularly uses Twitter to pursue his various political and social agendas—he is clearly thinking about succession.

In the wake of the phone-hacking scandal in the U.K., in which The News of the World had been accused of hacking the phones of a number of celebrities and members of government, James Murdoch’s future with his father’s company was unclear at best. There was even speculation that Murdoch senior might either pick someone outside the family to run some of his business operations, or hand the reins to his other son Lachlan.

At one point, Lachlan was the one who was supposed to inherit control, and was even referred to by some inside the company as “the prince.” But he and his father clashed while he was deputy chief operating officer of the holding company, where he felt his every decision was being second-guessed by his father or his lieutenants, and he eventually moved to Australia. Rupert lured Lachlan back into the fold last year when he was made non-executive chairman of both News Corp. and Fox.

For his part, Rupert has maintained that he never wavered in his support for James—telling Fortune’s Patricia Sellers in an exclusive interview that his son had performed his management duties admirably:

“Everyone talks about hacking in London. That all happened long before James took charge,” Murdoch told Fortune. “He took STAR television and [made it] the No. 1 broadcaster in India, with about eight channels, and is making a big difference to that country. He completely changed BSkyB and lifted the bar there in every way—and added huge value to News Corp.”

Despite this paternal praise, the big risk for Fox at this point is that the ascension of James could result in the company losing its “adult supervision”—that is, Chase Carey, whom many have seen as the real power behind the Murdoch throne. According to a number of reports, Carey will leave his official position, but will remain as an advisor to Rupert (according to CNN Money, Fox News chairman Roger Ailes will also continue to report to the elder Murdoch rather than James).

Keeping Carey around, even in an advisory position, could be a critical factor for the stock price. Laura Martin of Needham and Co. told Reuters: “The most important thing in the immediate term is that Chase Carey not leave,” adding that “if the implication of Rupert handing the title to his son is that Chase Carey leaves in the near term, we would expect that to negatively impact the stock prices.”

The Murdoch family currently owns a little over 10% of the shares in both News Corp. and Fox (which has a market value of about $67 billion), but control close to 40% of the voting power through their ownership of class B multiple-voting shares. That means they have effective veto power over the future of the company and the board of directors.