Before it announced the global change of policy, HSBC had begun sending letters to U.S.-domiciled clients with accounts in India, saying they would need to close their offshore accounts. In April, a New Jersey businessman named Vaibhav Dahake pleaded guilty to conspiring with bankers at HSBC to hide money in India from the IRS.

Asked about the Dahake case, HSBC spokeswoman Juanita Gutierrez said, "HSBC does not condone tax evasion, and we have no further comment."

Independent registered investment advisors such as Constellation controlled 11.5% of the $13.4 trillion U.S. wealth-management market in 2010, up from 9.5% in 2007, according to data from research firm Aite Group LLC in Boston. Brokers from the largest banks manage 38%, down from 41% in 2007, Aite says.

By any measure, catering to the wealthy is a growth business. The number of individuals worldwide with $30 million of liquid assets to invest rose 10.2% to 103,000 in 2010, according to a June report by Cap Gemini SA and Merrill Lynch Global Wealth Management, a unit of Bank of America Corp. That $30 million club controls $15 trillion of capital in total.

Getting clients with big money doesn't mean you're going to make big money, says Elizabeth Nesvold, managing partner at Silver Lane Advisors LLC, a New York-based investment bank that specializes in mergers and acquisitions of wealth-management companies.

The heavy increase in competition means many new family offices are willing to cut rates, she says. Most charge annual fees equal to a percentage of a family's liquid assets; 0.35% to 0.75% is the normal range, according to the Family Office Exchange.

Labor-intensive work such as taking a client's son or daughter on a college tour is often included in the fee, Nesvold says, and if those tasks multiply, profits go down quickly.

Bessemer had a profit margin of 13% in 2010 compared with 21% at Goldman Sachs Group Inc., whose internal family office is called Ayco Co. (Goldman chose not to participate in the ranking.)

Bessemer is owned by its employees and the descendants of Henry Phipps, a partner of Andrew Carnegie. Phipps started the firm in 1907 to manage his proceeds from the sale of Pittsburgh-based Carnegie Steel Co. Bessemer now serves more than 2,000 multigenerational families.

John Hilton, CEO of Bessemer, says the advantage of working for a private firm like his is that there are no shareholders to satisfy. And it means he can go the extra mile for his clients. One of his employees once waited in line at the Department of Motor Vehicles in New York for a client who had just moved to the city and needed a license. The Bessemer staffer called the client as she reached the front of the line.