Some will be frittered away. “A lot of these ultra-high-net-worth individuals are men aged 60 to 70,” David Friedman, president of the research firm Wealth-X, says. “They’re sensing their mortality now. And there’s a growing wave of liquidity that’s going to fuel luxury and fuel philanthropy in a way that the market’s never seen.” Extravagant bucket-list items will be crossed out (with so many engraved Montblancs), but a great deal more will be left to children in the form of family businesses, estates, real estate and so on.

A study by the consulting firm Accenture identifies precisely when that shift might peak, starting in 2031. The firm looked at inheritances generation to generation. The baby boomers received a “great transfer” of wealth from their parents. And Generations X and Y will take a greater wealth transfer from the baby boomers, in time.

When that process is underway, 10 percent of the country’s total wealth will change hands every five years through inheritances, estates, gifts and the like. And as income and wealth have become distributed less evenly, the inherited spoils will be distributed unevenly, too. Households with less than $500,000 in net worth will transfer about $3 trillion to their heirs. Ones with more than $500,000 will transfer four times that much wealth.

That money will flow into the bank accounts of the by-then-over-the-hill members of Generation X and Generation Y, and the United States might look a little more like aristocratic Europe, with its Downton Abbeys and super-hyphenated names — maybe with a few more tattoos. Lists like the Forbes 400 might be filled less with financiers and technology entrepreneurs and more with third-generation Waltons and second-generation Zuckerbergs and Bezoses or, perhaps, first-generation Walton-Zuckerberg von Bezoses.

If income inequality continues its upward trend, a new generation of the superwealthy could come to crowd out those inheritors. Not only does family money get chopped apart as it passes from generation to generation, it has great potential for self-destruction. The same story plays out a thousand different ways: Hardscrabble grandfather makes the money, Junior sustains the business while living well all his days and then the Third, softened by a charmed life, fails in his duties as scion. “There’s a phrase: ‘Shirt sleeves to shirt sleeves in three generations,’ ” says John Davis of Harvard Business School, who studies family wealth. “I’ve worked with families in 60 countries. They’ve all got some version of the same saying.”

But it does not seem to matter too much one way or another. Inheritances are just one way that wealthy families help out their children; and not the most important one, either. So-called “inter vivos” gifts help ossify a given child’s social, educational and professional status long before inheritances kick in. Miles Corak, an economist at the University of Ottawa, says the children of the rich benefit from birth: less-stressful home lives as toddlers, expensive education throughout their lives, well-timed donations to alma maters, full Rolodexes on graduation, help with that first down payment, and so on.

That might be one reason that American social mobility seems so stuck, with the odds of escaping poverty half what they are in countries like Denmark. But recent research has suggested that, contrary to conventional wisdom, rates of mobility have not actually declined as inequality has increased. Once that big wave of money hits in 2031, reality could bend more toward expectation.