St Andrews University could breach stringent intake guidelines because buoyant applications mean that it need not go into clearing this year.
Potentially, the university faces severe penalties from the Scottish Higher Education Funding Council if it overshoots intake targets by more than 3 per cent.
The university had an unprecedented 44 per cent increase in home-student applications following the revelation that Prince William was to study history of art there from this autumn.
Generally, some 5 per cent of its first-year intake is filled through clearing. But this year the university has filled every place already.
Stephen Magee, St Andrews director of admissions, said the university could not say what the final intake would be as it was still matching examination results to offers and some students offered unconditional places might not take them up.
"It will only be by mid-October that we have a firm grip on absolute numbers," he said. "But, at the moment, we don't anticipate a serious breach of the funded numbers of home students."
St Andrews' target for full-time home students is 4,063 for the coming year, and it can go up to a total of 4,185 before Shefc considers clawing back funds.
St Andrews hopes that if it exceeds the guidelines, Shefc will treat this as "exceptional circumstances" and waive any sanctions. If not, it will not be funded for any overshoot and will suffer a fine of the cost of the extra students' fees.
* St Andrews was at the centre of an anthrax scare this week as emergency services were called in to deal with a suspect package delivered to the institution.
St Andrews was on a list of four centres targeted to receive packages purporting to contain the virus. In the event, the suspect package did not contain anthrax.