The survey of 150 people around the world, conducted by Boston Consulting Group (BCG), found that the average wealthy individual maintains relationships with2.8 private banks, whileonly 20 per cent maintained a single private bank account.

The findings challenge the widely accepted view that the world's wealthy forming trusted relationships with private bankers, who provide them with discreet advice about a range ofmatters.

Instead, rich people are more likely to spread their assets between different banks to take advantage of different specialisations and to diversify their risks.

The findings have wide-ranging implications for the world's largest private banks, many of which are trying to position themselves as trusted advisers to the world's rich.

"Wealthy clients often see banks fulfilling different roles," said Christian de Juniac, head of private banking and asset management at BCG. "But I'm not sure that bankers sufficiently understand that they are often one of three or four serving the same client."

Financial institutions around the world are aggressively expanding their private banking operations in an attempt to take advantage of growing demand from rich clients for sophisticated products and personalised service.

Banks are also betting that the business, which is still highly fragmented, will allow them to benefit from economies of scale as they sign up more clients.

According to BCG, the total wealth controlled by individuals with assets of more than $100,000 expanded to $88,300bn last year, an increase of 8 per cent.

The greatest growth was in Europe, where wealth expanded 13.1 per cent in local currency terms, while growth in North America was just 4.1 per cent.

The BCG study found that rich people often have different aims when it comes to accumulating or preserving their wealth.

Some also want to be heavily involved in investment decisions, while others are happy to delegateeverything to their private banks.

However, private banks are slow to recognise these differences: "I don't think private banks have recognised what sort of clients they have and developed a service model that suits these individuals," Mr de Juniac said.

BCG expects the assets controlled by the world's wealthiest people - those with assets of $5m or more - to grow by 50 per cent in the next five years.