Nicola Horlick - or "supermum" to the tabloids, owing to the fact that she has high-flying jobs and five kids - has spent her career amassing a reported £25m; she now seems determined to divest herself of large parts of it. She already gives away about 25% of her income each year; she has just revealed, in a thinktank report on the state of philanthropy in the City, that she will not be leaving most of the remainder to her children. "I think it is wrong to give too much inherited wealth to children," Horlick told the report's authors. "I will not be leaving all my wealth to my children because that would just ruin their lives."

She is by no means the first to go public with this conviction. Bill Gates has ploughed an estimated $30bn into the Bill and Melinda Gates Foundation. This was supplemented, in 2006, by another £24bn or so from his friend Warren Buffett. (Buffett has always been colourfully, quotably clear on where he stands. His daughter often tells a story of finding herself without change for a car parking ticket - her father lent her $20, then promptly made her write him a cheque. "To suggest that the children of the wealthy should be just as wealthy," he has said, "is like saying the members of America's 2004 Olympics team should be made up only of the children of the 1980 Olympics team.") Anita Roddick, the late founder of the Body Shop, "told [her] kids that they would not inherit one penny. The money that we make from the company goes into the Body Shop Foundation, which isn't one of those awful tax shelters, like some in America. It just functions to take the money and give it away." Sir Tom Hunter, the first Scottish billionaire, announced last July that he will be giving his billion to charity; two weeks ago Barron Hilton said he would be doing the same with 97% of his $2.3bn fortune - his granddaughter Paris's embarrassing antics having convinced him that bequeathing unearned wealth is not something he wants to do.

He is fighting something of a rearguard action: what all these parents are keen to duck is the possibility of producing a Paris in the first place. "Advisers to the rich structure entire symposia for their clients around the idea of avoiding her fate," noted a recent piece in New York magazine. Horlick says she wants her children to understand "that there is more to life than shopping on the King's Road and mobile telephones"; Roddick is on record as boasting that her kids have "got one huge dose of what real thinking is, what real life is. They're not rich bitches snorting cocaine every time they go into a bloody club, they're not in bloody Hello! magazine. They work. They're real."

Britain may not have quite caught up with America, which has so many super-rich that there is a market for such symposia, and for outfits such as Tiger21, "a peer-to-peer investment group on the Upper East Side whose barrier to entry is investable assets of at least $10m" - but Britain is swimming in more wealth than ever before. Last year alone, the number of Britons with investable assets of $1m or more grew by 8%, according to a study by Capgemini and Merrill Lynch. According to Barclays Wealth, which provides its clients with advice on estate planning, the number of households with financial assets (excluding property) in excess of $1m is expected to triple by 2016. "There are so many more people than there have ever been who have more money than will ever be required to live on," says Merryn Somerset Webb, editor of Moneyweek and author of Love Is Not Enough: The Smart Woman's Guide to Money. "That's what throws up the problem." And the evidence (again, American) is that the richer you are, the more you worry about it - and the lower the proportion of your assets your children receive. According to a research paper published in the journal Philanthropy by the director and two staff members of the Boston College Centre on Wealth and Philanthropy, "As net estates become very large, wealth-holders make a conscious decision to move their resources away from heirs and towards charity." In 2003 heirs received 86% of the smallest estates ($1-$2.5m), and only 31% of the largest (over $20m). This is partly, and obviously, a function of the sheer amounts involved - 86% of $2m is $1.72m, while 31% of $20m is nearly four times as much - but it is instructive nonetheless.

Many of these rich do not come from riches. They are self-made, and generally the self-made have a different attitude to money - or specifically, the acquisition of money - compared with those who have always had it. They generally do not, for example, have the "legacy assets" of the old rich - the 4,000-acre pile in Scotland that has been in the family for generations and must be passed on in good nick; or the idea of noblesse oblige that used to go with such assets: the responsibility to the tenants of the land, to the local community. "With inherited wealth, the current generation may simply consider themselves custodians for the time being of the family wealth and will follow the path laid down over many generations," says Stuart Chappell, director of Barclays Wealth. "With self-generated wealth, it is the responsibility of those who made the wealth to decide what is to happen after they are gone. It is more likely that the creators of new money will feel that those who follow them should not be 'feather-bedded'."

While these new rich may see no harm in showering children with all the things and freedoms that they themselves could not have, they are more likely to feel that if they could, through skill and application, make a fortune, there is no reason why their children cannot do the same. But what if they don't want to? What if they do not have the same luck? "The self-made tend to believe, I think probably rightly," says Somerset Webb, "that work is a value in itself, and therefore their children not just should work, but need to work." In this rather Protestant world-view, money is simply a facilitator. According to Buffett, "A very rich man might leave his children enough money to make it possible for them to do almost anything they want, but he would be a fool to leave them so much money that they ended up doing nothing at all."

Increasingly, even those who make no grand stands about how "little" they are leaving their children are trying to control how much these children will receive. According to another report from Barclays Wealth, in association with the Economist Intelligence Unit, almost 60% of those with more than $10m in assets stipulate that a child must get a college education, or hold down a job for a prescribed length of time. The traditional age of accession to fortune might in the past have been 21, as we know from no end of Victorian novels; now it's more likely to be 25, or 30, or 35.

For all the obvious advantages of wealth, what's at stake is something more nebulous, less biddable: happiness. Somerset Webb ends Love Is Not Enough with a salutary cruise through the research on money and happiness. In the past 30 years, for example, our incomes have risen by 80%, in real terms - but according to research by the editor of the Journal of Happiness Studies, Ruut Veenhoven, we are only 1.36% happier. The major route to happiness, discovered a team from Gothenburg University in Sweden, was goal-oriented work; the successive positing and achieving of specific challenges. As Paul Sykes, a former tyre-fitter from Barnsley who is now worth £250m, has put it, "I have never found a link between money and happiness, but I have found a link between success and happiness." He claims that his son and three daughters will get nothing from him at all.

"Nothing", in this context, is, of course, relative. Even those who inherit nothing in financial terms will - unless their parents are particularly obtuse - have already received a priceless start in terms of education, lifestyle and opportunity. "I would argue that when your kids have all the advantages in terms of how they grow up and the opportunities they have for education, it's neither right nor rational to be flooding them with money," Steve Forbes has said. Hamish Ogston, a Yorkshire-based entrepreneur worth about £400m, has been just as clear: "I'm a firm believer in them having a leg-up in the form of reasonable parenting, education and possibly a few thousand pounds, but nothing much more than that."

But how much of a leg-up is enough? Ogston may think a few thousand pounds; it was reported last year that to live the way a millionaire's child might be accustomed - maids, yachts, jewellery, second and third homes - now requires not a million but £5.8m. "If you happen to be a multibillionaire, you might think you're being cruel to your children by leaving them less than, say, £5m," says Somerset Webb. "Whereas if you only have a couple of million, you might think that leaving them enough to put a deposit down on a flat is plenty. So it's still an area of huge extremes, and when Nicola Horlick says, 'I'm not leaving all my money to my children,' it's impossible to know exactly what she means - buy them all a central London flat and be done with it? Or does she mean that they'll get £5,000 and a secondhand car? Who knows?"

Get it wrong, however, and you could be dealing with anything from damage control of Hiltonesque proportions or the self-destructive excesses of the Marquess of Blandford (whose behaviour led in 1994 to him being stripped of his right to the Marlborough estate, which includes Blenheim) to, more usually, a low-key, chronic sense of disappointment and failure. A psychologist quoted in New York magazine found that in a sample of 314 tenth-graders in a wealthy suburban community, the rate of "clinically significant anxiety" was 5% to 9% higher than the norm while, among girls, the rate of "clinically significant depression" was three times the national norm.

"The pros of inheriting great wealth, I believe, are largely illusory and can become pathological," Sigrid Rausing, whose family is worth an estimated £5.4bn, recently told the Economist's Intelligent Life magazine. "An illusory sense of being special and different, the assumption that one is interesting to other people only, or mainly, because of the money, and subsequent feelings of isolation." The children of the rich know that this will not elicit much sympathy from the hordes who would dearly like a tad more cash to ease their passage through life, but the feeling that there is nothing to aim for, nothing to achieve (or, conversely, when parents have achieved so much that their children cannot imagine matching them), is corrosive of self-worth. People with average means who aspire to write the perfect novel, for example, or to be a great actor, might give it their all for a couple of years and then give up (or at least get a complementary job), admitting they hadn't made it and moving on to something more fulfilling - whereas having so much cash that you never have to do this creates "a position of constant failure", as Somerset Webb puts it. Unhappiness and lostness in turn result in guilt: how is it possible to be unhappy when you have so much? And that, too, is corrosive.

Get it right, and enough can be not just good, but fantastically enabling. Somewhat inevitably, the piece in Intelligent Life ends by reminding its readers of Virginia Woolf, her discovery of the absolute importance, for a woman, of a "room of one's own", and the comparatively modest £500 a year (£20,500 today) needed to achieve it. "My aunt's legacy revealed the sky to me." Entrepreneurs can take risks they otherwise mightn't; investors can subsidise imaginative startups; the altruistic can help others without the overwhelming need to help themselves first. And the enabling applies however modest their aspirations. "When I think about the people I know who have inherited money," says Somerset Webb, "the ones who have used it right are the ones who live perfectly ordinary lives, just slightly better." Now that's something probably worth envying.