Which countries?

Wikipedia is your friend: Public University

And I hope I'm not expected to know by heart the educational systems and immigration policies of all the countries in the world? I'd expect most publicly-funded universities would be for citizens' (or atleast permanent residents') children, as it's those people that pay the taxes that fund the university.

But that's the sort of subject that you should investigate yourself, not take my word (and guesswork) for it.