As bigger sums are invested overseas, one thing can be predicted with certainty. The tax bill will be greater and more will be withheld by the authorities.

Withholding tax is deducted from dividends paid to non-residents. This may be reclaimed if there are tax treaties between countries.

But calculating quite how much tax is kept back is far from a simple exercise, either for custodian banks or those who have entrusted their money to them. Taxmen the world over make sure the tax element on dividends and interest is paid direct to them, with the onus on investors to reclaim.

Tax rates vary from country to country, as does the amount withheld. Taking just three European neighbours: France deducts 15 per cent, Switzerland 35 per cent and the Germans a very precise 26.375 per cent.

Amounts can also vary depending on whether the money is invested in bonds or equities, and the exact nature of the double taxation treaty in force between withholding nations and the investor's country of residence.

Big custodian banks may each make up to 30,000 individual reclaims a week. Before computers, that task would have required more than 120 clerks.

The figures help explain why tax reclamation is such a complicated business, historically kept well to the rear of most back offices.

But the sheer size of the sums involved are now bringing reclaims further towards the front. Tax recovery is becoming an important competitive factor for fund managers in determining performance figures.

Every holding in a portfolio, whether in shares or bonds, requires a separate tax reclaim. "So it only becomes worthwhile when the amount recovered is worth more than £75 per transaction," says Damon Holliday, director of London-based tax software producers Global Equities.

Ross McGill, chief executive of Goal, another software specialist, believes $35m and more is lost worldwide in non-reclaimed tax every year.

He fears more money may be forfeited thanks to draconian measures introduced by the US taxman at the beginning of this year.

The IRS rules break new ground in requiring custodians, other banks and fund managers to become approved Qualified Intermediaries. Only they can make reclaims on behalf of clients.

According to Andrew Tucker, a partner in custodian bank Brown Brothers Harriman: "The new regulations pass much of the reporting burden down the chain to the intermediary."

Although several thousand investment organisations should have registered, Mr McGill says about only 1,000 have yet done so - about half of the end-June target. Failure to meet the accounting regulations could prove expensive, for the IRS will deduct and retain tax at rates of up to 31 per cent.

Its objective is to detect US citizens investing in US securities through an overseas nominee. But everyone is caught in the net.

However, it will be the end of 2003 before the impact of the new procedures become clear, says Mr Holliday. "Other countries are watching the US experiment closely," he says.

And Ross McGill reports that Japan will soon announce its own QI system, which will have a huge effect on the industry.

As Andrew Tucker says, "a comprehensive and effective tax service will become a key selection criterion in looking for a custodian".