As it was announced the overall pass rate for A-levels has risen for the 30th successive year, many institutions in Scotland entered the clearing system, which matches qualified students with places.
The most popular universities – including Edinburgh, Glasgow and St Andrews – do not need to enter clearing because they already attract significant interest from students from the rest of the UK (RUK). However, institutions including Aberdeen, Dundee, Napier and Heriot-Watt in Edinburgh, Stirling and the University of the West of Scotland all advertised places on hundreds of courses including languages, physics, economics, history, law, English, philosophy and fine art.
The ability to attract RUK students is now more important than ever for Scottish university funding because they pay fees of up to £9000 a year and places are uncapped.
However, contrary to some reports this week, the availability of places for RUK students has no bearing on Scottish places, which are considered separately and have been maintained in line with previous years.
Nonetheless, NUS Scotland, which represents students, said the Scottish Government should consider expanding higher education in future.
It expressed concern Scottish students still looking for a place would be angered at the large number of places now being made available for fee-paying students.
Robin Parker, president of NUS Scotland, said: "When Scottish students are being turned away from clearing while counterparts from across the Border are being welcomed with open arms, I can entirely understand why students in Scotland will feel aggrieved.
"We need to do everything we can to increase the numbers of Scottish students able to go to university in Scotland."
However, Universities Scotland, which represents university principals, said there was no evidence significant numbers of suitably-qualified Scottish pupils were being "turned away".
Alastair Sim, director of Universities Scotland, said: "The number of places available to Scots – and EU students – is controlled by the Scottish Government and the Government has acted to protect the number of places available to Scots.
"We continue to offer the maximum number of places possible to Scottish applicants and the vast majority of well-qualified Scottish applicants who want a place at university in Scotland will get one."
Overall, figures published yesterday by Ucas, which runs the clearing system, showed Scotland is the only part of the UK to have increased the number of students going to university, with acceptances to Scottish institutions up by 0.7% compared to an 8% decrease in England, a 5% drop in Wales and a 4.5% reduction in Northern Ireland.
A Scottish Government spokesman said: "It is completely wrong to suggest Scottish applicants are being put at a disadvantage. The fact universities can now charge students from the rest of the UK has had no bearing on the number of places available to Scottish students. Places to students from the rest of the UK are considered separately and are additional to this."
On average, some 30,000 Scots go to university every year in Scotland compared to some 4000 from England, Wales and Northern Ireland and 4000 from the rest of the EU.
The number of school-leavers from Scotland going to university has expanded over the past 20 years from 18% to 48%.