We present a model which allows us to show that stratification of public universities, accordingto the quality they offer and the quality of students they select, is a plausible result even in a pub-lic university system where tuition fees are uniform and decided by the administration. This resultis similar to that observed in private and competitive university systems. We prove that it is veryunlikely that segregation and stratification could be avoided by subsidizing those universities thatare more inefficient. We show also that even if stratification and segregation could be removedthrough subsidies, it would be at the cost of reducing quality of education at the whole universitysystem.