Does a public university system avoid the stratification of public universities and the segregation of students?

We present a model which allows us to show that even in a public university system where tuition and fees are fixed by the administration, a stratification of public universities according to the quality they offer and the quality of students they select, can be observed. This result is similar to that observed in private and competitive university systems. We also show that it is very unlikely that segregation and stratification could be avoided by subsidizing those universities that are more inefficient. We show also that even if stratification and segregation could be corrected with subsidies it would be at the cost of fixing the upper-bounds at the quality that could be offered at any university, hence fixing quality limits at the whole university system.