After Auckland and Otago on the funding table come Massey, Canterbury, Victoria, Waikato, Lincoln and Auckland University of Technology.
Dr John Hood, vice-chancellor of the University of Auckland, said the report showed Auckland led research "on virtually any measure".
The results reflected staff's ingenuity, creativity and hard work, he said.
The other 16 institutes - a mix of polytechnics, colleges of education, wananga and private education providers - share 1.6 per cent of the funding.
The total funding this year is $18 million, 10 per cent of the total $180 million that the fund will distribute once it is fully phased in by 2007.
Under this year's figures, universities gain 5 per cent more than under the previous system, while the other institutes lose between 67 and 87 per cent of what they used to get.
The new system grades all academics on the quality of their research, from "A" for world class to "R" for "research inactive".
About 450 of the 8013 people assessed gained a world-class grade.
The top research subject was philosophy, followed by anthropology, archaeology and earth sciences.
Bottom were nursing, design, education and sport and exercise science.
The funding formula works by using the grades to determine which institutes are doing the best research.
"The PBRF results reveal significant strength in most of the country's universities and in many subject areas," said acting commission chairwoman Kaye Turner.
"It provides a powerful new incentive for tertiary education organisations to concentrate their research around areas of excellence."
The system has attracted criticism and controversy.
A comparison with English universities' performances was blocked after legal action by Auckland and Victoria Universities.
Other institutions said the system penalised institutions and subjects where research was not fundamental.
It was also likely to give some skewed results because organisations with one excellent researcher could score higher than institutes with hundreds of good researchers, they said.
The final funding table takes this into account.
But a second table in the report, directly comparing research performance, shows Penrose's Carey Baptist College and Anamata, a private training establishment for Maori in the Bay of Plenty, have better-quality research than Auckland University of Technology.
AUT vice-chancellor Derek McCormack said he was not surprised.
"I think those very small institutions can do well on average," he said.
"But if you look at the category areas, we are not the last university by any means in all of them."
Anamata chairman Tamati Kruger said the institution had produced groundbreaking research identifying skills required for social workers dealing with family violence in the Maori community.
Associate Tertiary Education Minister Steve Maharey said the results confirmed that world-class researchers were spread across almost all the major academic fields.
"Right now, it's important that everyone with a stake in the standard of research in our tertiary education institutions takes a hard look at the results and asks what the results really mean, where the opportunities for improvement are and what can be done next."
He said the PBRF enabled the Government to "move away from a crude 'bums on seats' approach to funding research".
Tertiary research
* The Government has set up the Performance-Based Research Fund for tertiary research.
* This year the fund is paying $18 million, or 10 per cent of the research component of existing Government grants to tertiary institutes.
* This will rise to 100 per cent of the research grants ($180 million) by 2007.
* Universities will receive the lion's share of the fund.
Evaluating Research Excellence: the 2003 assessment
Herald Feature: Education
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