Mr. Fink maintains a grueling schedule, mixing regular bicoastal trips in the United States with frequent client jaunts to China and the Middle East. “This job requires an enormous commitment,” he said. “The pace is relentless. There will be a day when I wake up one day and say I just can’t do it anymore.”

That day remains well in the future, he says. Still, with BlackRock’s growth in size and sway, the issue of who, if anyone, from within the firm is qualified to succeed Mr. Fink has become an existential question for the company’s board of directors.

The problem is typical when replacing a founder: Mr. Fink has increased assets to $5 trillion from zero, and the imprint of his domineering personality has become so profound that virtually anyone will suffer to some degree in comparison, considering his track record.

After all, in 1983, he structured one of the first collateral mortgage obligations, and along with Lewis Ranieri at Salomon Brothers made it possible for large investors to enter the market for mortgages. A quarter of a century later, Mr. Fink recognized that the time was right for E.T.F.s and — in the depths of the financial crisis — bought Barclays’s iShares business, a deal analysts consider one of the shrewdest in recent Wall Street memory.

And beyond a soaring stock price, there are few better ways for a financial chief to command the respect of his peers than to slip through the grasp of regulators. So when Mr. Fink and his high-powered lobbyists in Washington were able to make the case, after the 2008 financial crisis, that major fund companies like BlackRock posed no risks to the markets because of their size, it only added to his aura.

There is a moment in Don DeLillo’s “Cosmopolis,” his meditation on the alienating effects of money and machines, when the protagonist financier offers a bit of advice to a colleague. There’s only one thing worth pursuing professionally and intellectually, he says: the interaction between technology and capital — its inseparability.

That, more or less, is what Mr. Fink told Dexter Senft, his computer expert at First Boston in 1982. “We are bringing the computer onto the trading floor, Dexter,” Mr. Fink recalls saying at the time. “If we can do this, it will change our business forever.”