Do liberterians believe STATES should have public schools, state universities, healthcare and poverty...?

The state has the right to decide about this issues. Though, this ends in a wide array of problems and mismanagement. It proves that the public sector isn't equipped to handle these problems. About public schools, they will still exist even if the Department of Education is abolished. I as a libertarian don't hate public school (went to one my whole life). The problem with these programs is like we see in New Jersey (my state). The state has debt problems, it has the third highest debt in the nation. Corzine wants to privatize the turnpikes so he could reduce costs. That is how bad we are as a state! NJ is a liberal state, with programs like you mentioned. But families are moving out, property taxes are extremely high and I'm not even a homeowner but they do have it tough. To answer your question the states do have the right to have these programs but how will they fund it? By forcing people like do for everything? Having monetary problems and to look for ways to subsidize these programs because too many people depend on it? It all ends badly.