Earlier this month, several of the most important players in the private banking sector—a clubby, secretive group serving uber-high-end clients—gathered for a summit in Singapore.

The location of the meeting was hardly accidental. As Swiss banks have seen dramatic outflows after a regulatory crackdown, Singapore has asserted itself as the new kid on the block in the private banking sector. According to the Boston Consulting Group, Singapore now has $500 billion in private banking assets, up from $300 billion in 2008.

There’s one overriding reason for Singapore’s private-banking boom: Asians are getting richer, and more numerous. The number of high-net worth individuals in China and India will nearly triple in the decade ending in 2018, adding about $4 trillion in individual wealth, according to a Merrill Lynch/Capgemini study. Singapore, with its central location and stable government, is a logical place to go. India and China are viewed as too risky, and many investors fear that Hong Kong is increasingly under the purview of Beijing.

Singapore has been anticipating this shift—and working to catalyze it. Since the 1997 Asian financial crisis, Singapore’s government has made a concerted effort to boost the city-state’s financial infrastructure. In 2000, Singapore strengthened its bank secrecy laws, promising clients total privacy. It helps that there are no taxes on capital gains, and that depositors are able to open accounts in the guise of corporations, trusts, and limited liability corporations, which is how most ultra-high-net-worth individuals manage their money. The government also offers tax incentives to companies setting up their regional headquarters in Singapore.

Although the world of private banking changed last year — when the U.S. government charged UBS with fraud and demanded the names of around 5,000 wealthy, tax-evading U.S. clients –insiders say Singapore has been little affected. It is on the OECD’s “gray list” of offshore tax havens that foreign governments are threatening to scrutinize further—and so has agreed to comply with Tax Exchange Agreements and assist foreign governments with criminal investigations. But the countries that seem to care most about onshore/offshore banking are not the home governments of Singapore’s richest account holders (e.g. India, China, and Indonesia).

Private banking goes mass market

Little wonder, then, that global banks have been ramping up their regional private banking operations in Singapore. Morgan Stanley said last month that it plans to double its Asia head count in wealth management over the next three years. Credit Suisse’s head of private banking recently told Reuters Insider that new assets from rich Asian clients will exceed its growth forecasts, increasing by more than 20% by the end of 2012. “We expect to end the year with 25% growth in assets under management,” says Rajesh Malkani, the regional head of private banking in Singapore for Standard Chartered Bank.

The rush has also brought some interesting side-stories. As in any rapidly growing industry, demand for talent in private banking outstrips supply. As a result, insiders complain that too many private bankers working on the Singapore scene are playing musical chairs, jumping from company to company at first sight of a sweeter pay package. In 2007, there were stories out of Hong Kong that well-connected hairdressers would be turned into private bankers.

Now, the industry is showing evidence of having matured a bit. “The simple request will always be, give me a relationship manager with at least $150 million in assets under management,” says Declan O’Sullivan, managing director of Kerry Consulting, a headhunting firm.

Further evidence of a maturing industry is an increasing number of smaller players. Some insiders say Singapore, like Switzerland, is taking private banking mass market. A check for $2 to $3 million can open an account in a private bank; the typical $20 million check is no longer required.

And that broadening of the industry, circularly, has made room for even more jobs—which Singapore is happy to fill. The Wealth Management Institute, conceived in 2003 with the help of Singapore’s two sovereign wealth funds, GIC and Temasek, has graduated 2,500 students from its courses since 2004. “This year, we’re already experiencing more than 50% increase in enrollment in our programs for 2010,” says Cynthia Teong, the institute’s Executive Director and CEO.

The upshot is simple and clear. Whatever happens to Switzerland, the financial services industry will morph as needed to make sure that the world’s super-rich are well taken care of.