An article by CNBC's Robert Frank

Forget investment returns, spending rates or divorce. What really keeps the rich up at night? The fear of ruining their kids with wealth.

A new survey by law firm Withers LLP and Scorpio Partnership asked 3,000 families around the world about their greatest fears regarding their wealth and family future. Among families worth $10 million or more, health was their biggest fear. But ranking second was, "My children will lack the drive and ambition to get ahead."

The spoiled kid issue ranked ahead of "my investments," "I or members of my family will overspend" and "marital breakdown."

"For parents, the main concern is that great wealth will scotch the individual ambition in their children," the study said. "Meanwhile, it is perhaps not surprising that children may feel somewhat inadequate in matching up to expectations when you consider the great heights of achievement their parents have scaled."

The study didn't provide any solutions and suggested that no matter what rich parents try to do, large wealth can strain the family.

"Several families had become estranged over the years," it said. "Some families said this was because they had given their children too much, and some said it was because they had given too little."

The results come after pop singer Sting said that he won't be leaving "much" of his $300 million fortune to his six kids.

"I told them there won't be much money left because we are spending it," he told the Mail on Sunday Event magazine. "I certainly don't want to leave them trust funds that are albatrosses round their necks. They have to work."

Bill Gates, Warren Buffett, Sandy Weill and other members of the wealth ranks said they prefer to give their fortunes to philanthropy rather than creating multigenerational dynasties. They are still leaving substantial amounts of money to family members; but, as Buffett once said, he planned to give his kids "enough money so that they would feel they could do anything, but not so much that they could do nothing."

The effects of wealth on children is likely to get even more attention with what a recent study called the greatest wealth transfer in history. A study from the Boston College Center on Wealth and Philanthropy projects that $36 trillion will pass down to heirs between 2007 and 2061.

So far, however, evidence of a huge cascade of inherited wealth has yet to materialize. Between 1989 and 2007, the share of households reporting a wealth transfer fell by 2.5 percentage points, according to a study by NYU economist Edward Wolff that looked at tax returns.

As one wealth creator in Asia said in the Withers study: "To bring a whole family along, you need clarity of purpose. You need to live your values, don't intellectualize them. You must correct power imbalances when they occur in the family. And, remember that money does not confer wisdom. You are lucky, not smart and your children must know that they are lucky, not smart."

—By CNBC's Robert Frank