Mr. Murdoch must have known he needed to get even bigger to survive. But lately his buying prowess has taken a hit. In 2014, investors rebuffed him when he tried to gain scale with an $80 billion offer for Time Warner Inc., the company that owns HBO and CNN — and which may end up the property of AT&T, if a deal long in the making survives the scrutiny of a skeptical Justice Department. Regulatory hassles have also thwarted Mr. Murdoch’s efforts to pay $15 billion for the 61 percent stake in Sky not already owned by 21st Century Fox.

“He tried to buy, and when that didn’t work, he doesn’t sulk — he sells,” Ms. Martin said.

Disney’s planned acquisition of 21st Century Fox — Mr. Murdoch’s confidants call it a merger — makes economic sense, analysts say, and may be the best way for Mr. Murdoch’s broader empire to thrive. But it also makes the identity of his heir less apparent.

Mr. Murdoch’s younger son, James, 44, has reinvented himself since an intense legal imbroglio in Britain that sprang up after the News of the World tabloid hacked into the voice mail of a 13-year-old murder victim. James Murdoch, who is said to be supportive of the Disney deal, left his post in London, moved to the United States and took over one of his father’s jobs: chief executive of 21st Century Fox.

Lachlan Murdoch, the elder brother at 46, has been caricatured as the prodigal son. He left the family business in 2005 and was happily living out of the fray in Australia, with a supermodel wife and a trust fund. But as part of Mr. Murdoch’s succession plan, Lachlan returned to the United States in 2015 to serve with his younger brother — and alongside his father, as co-executive chairman — at 21st Century Fox. Seen by some insiders as a daddy’s boy, he moved into his father’s former office on the company’s palm-tree-lined lot in Beverly Hills.

Questions abound about which son would carry on the family legacy, should the Disney deal go through. (Mr. Murdoch’s older daughters, Prudence and Elisabeth, have stayed mostly out of the business, and his younger daughters, Grace and Chloe, are teenagers.)

“You have this issue with two sons who are seemingly capable of commercial success and, if you’re Rupert, you want to leave them both in a good spot, for lack of a better spot,” said Brian Wieser, an analyst at Pivotal Research.