The number of foreign trusts has plummeted by three-quarters following the introduction of tougher rules at the beginning of the month.
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Inland Revenue (IRD) said it received applications to register fewer than 3000 trusts, while another 3000 told the tax department they did not want to be part of the new regime.
There were roughly 11,750 trusts at the end of last year.
Inland Revenue said the remainder - nearly 6000 - are unaccounted for.
Last year's revelations in the Panama Papers showing foreigners used New Zealand to hide their wealth embarrassed the government and forced it to take action after earlier saying there was no problem.
Under the new regime, foreign trusts will file annual returns. The information will include who owns the trust, what assets are in it and who the beneficiaries are.
IRD is also promising to pass on the details about those with New Zealand foreign trusts to other countries without being asked.
It will spend the next few months processing applications, and cross-match the new information against the disclosures under the old regime to find out where the unaccounted trusts may have gone.
Tax experts said it was likely the unaccounted trusts have been wound up or shifted to another jurisdiction.
A New Zealand foreign trust provider who was named frequently in the Panama Papers, Roger Thompson of the accountancy firm Bentley's New Zealand, said 80 percent of the foreign trusts his firm act for had registered on time, 14 percent were terminated and 6 percent changed to a trustee based outside of New Zealand.
"Generally this was because the trusts were largely inactive and the clients did not wish to incur the hassle and costs of re-registration. I'm not aware of a single case where the client was concerned about disclosure to government agencies," Mr Thompson said.