Over a dozen college courses have passed the 600 CAO points threshold, amid soaring demand for places.
The CAO received over 6,500 more applicants this year than in 2020.
First-round offers were sent out this afternoon.
Four courses - Dentistry in UCC; Management Science and Information Systems Studies and Dental Science at Trinity; and Economics and Finance at UCD - have hit the maximum points threshold due to demand.
Over a dozen others have points requirements in excess of 600.
In those cases, random selection means not all people who reached the required points were offered a place.
A student can only get a maximum of 625 points if they receive H1 grades across six higher-level Leaving Cert subjects including maths.
Higher maths is the only subject that offers an extra 25 points.
The increasing demand for college places and the record high Leaving Cert results are causing points to rise in a number of courses.
Irish Times’ Education Editor Carl O’Brien says the pandemic has also influenced people’s college choices.
He said: "Nursing, medicine as well as pharmacy and radiography... those high demand health courses, for the most part, will see point rises based on the trends we're seeing.
"That also goes for a lot of science courses too - perhaps the importance of vaccination has put this into the mind of students."