Fee-paying schools, typically charging €4,500-€6,500 for a day student, dominate the list of who sends the highest proportion of past pupils to third-level.
Many schools in the free education system match their record, but a big divide is seen when comparisons are made with schools with high concentrations of disadvantaged students.
The so-called league table is based on data provided by over 30 third-level colleges about the school of origin of students who enrolled this year on the basis of their Leaving Certificate results.
Because of the volume of information involved, there may be some discrepancies, but the table does offer a broad picture of progression to third-level among over 700 second-level schools.
As the table is published, a teachers' union has warned that such lists are hugely damaging to the inclusive school that admits all the children of the community.
The Teachers Union of Ireland (TUI) said inclusive schools were unfairly represented by so narrow a focus on third-level progression.
TUI general secretary John MacGabhann said the lists promoted a view that a school's success was solely dependent on students achieving entry to third-level courses that required high points.
"We believe that a school's mission is more expansive, inclusive and generous than such a narrow vision suggests," he said.
Mr MacGabhann said each individual student was unique and each had an individual set of talents. For many, completion of the Leaving Certificate itself was a major achievement.
"They may, for example, be the first generation of their family to do so. Others may have special educational needs and more again may be relative newcomers to Ireland with a first language other than English.
"The struggles and hugely impressive personal achievements of such students cannot be translated into cold, tabulated data," he said.
Mr MacGabhann noted that the lists did not provide information on whether individual schools offered programmes such as the Leaving Certificate Applied or Leaving Certificate Vocational Programme.
Nor did they provide information on students who had successfully progressed to apprenticeships, or to further education, such as Post Leaving Certificate (PLC) courses, he said.
"If third level access rates were the only indicator of the success or otherwise of a school, the true meaning of education would be severely distorted. "The publication of these lists inevitably leads to unfair comparison that is hugely damaging," he said.
A number of measures introduced or planned by Education Minister Ruairi Quinn are aiming to bring more fairness into the system.
He has cut state support for fee-paying schools by increasing the number of pupils they need before they are awarded a teacher.
However, many fee-paying schools are sitting on considerable financial reserves which allow them to pay for teachers privately.
He is also preparing legislation to ensure all schools take their fair share of pupils with special needs.