A record number of Scottish students will start university in the country this year.
A total of 22,292 Scottish students have received places so far, a 3% rise from 21,630 in 2011.
The Government said around 3000 applications are still being processed by the Universities and Colleges Admissions Service (Ucas) with more eligible for the clearing process, but critics have said the process is "unfair" as the number of places for Scottish students is limited by funding at some universities.
Scottish and EU students are exempt from tuition fees at Scottish institutions. However, a loophole in EU regulations means that students from the rest of UK have to pay to study in Scotland.
Universities are given set funding for the admission of Scottish and EU students.
Education Secretary Michael Russell said: "The case for keeping education free in Scotland has been proven beyond doubt. This year we have had the highest-achieving pupils sitting Highers and the highest number of young people secure their preferred university place since records began.
"The figures tell their own story. But it is not just about numbers, it's about the students themselves. We want to ensure every Scottish school leaver has the best opportunity to succeed and reach their full potential."
Robin Parker, president of National Union of Students (NUS) Scotland, said the number of places in the clearing process for Scottish students was limited because of limited funding for Scottish and EU students and the need for universities to attract fee-paying learners.
He said: "Students from England, Wales and Northern Ireland cannot take places away from Scottish students, and places for Scottish and EU students have been protected.
"However, 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.
"This is yet another example of the unfairness built into the new system of tuition fees for students from the rest of the UK.
"We've always said it's unfair on students from England, Wales and Northern Ireland to be asked to pay up to £36,000 for a degree, just as it is to ask anyone to pay fees for their education.
"This just shows the potential for unfairness for Scottish and EU students too."
A University of Edinburgh spokesman said: "The Scottish Funding Council allocates each university in Scotland a number of funded places for students from Scotland and the EU, and imposes financial penalties should institutions over-recruit against this number. The University of Edinburgh intends to fill all of its allocated places for Scotland and EU students this year."
Ucas figures also show that Scotland is the only part of the UK which has seen a rise in university and college admissions.
A total of 35,781 pupils have been accepted to Scottish institutions to date, fractionally up by 244 on this time last year.
Meanwhile, applications to institutions in the rest of the UK are down by almost 8%, from 349,112 at the same admission stage in 2011 to 322,134 this year.
The 13,489 extra admissions to Scottish institutions are comprised of pupils from the rest of the UK, who received their A-level exam results this week, and international students.
Mr Russell said: "Scotland is the only country in the UK to ensure young people, our workforce of the future, can go to university based on ability, not the ability to pay.
"We are also the only country in the UK with an increase in the number of total acceptances — compared to a significant decrease of 8% in England. And Scotland is the only place in the UK where every young person aged 16 to 19 is guaranteed a place in training or education."