BUFFALO, N.Y. — They don’t mean to sound ungrateful, but … New York public college students who would stand to gain from the nation’s most ambitious free-tuition proposal are quick to point out a sobering reality from their own meager finances: Free tuition doesn’t mean free college.

Take Brooklyn College senior Florencia Salinas, who despite having her tuition nearly covered in full through scholarships and grants, still expects to graduate with a daunting $50,000 in debt. Or Buffalo State College junior Avery Edwards, who despite similar financial aid expects to owe $20,000 after collecting his degree next year.

That’s because tuition, at around $6,500 a year, is just about a third of the typical four-year student’s total public college bill in New York. Room and board are the bigger-ticket items at nearly $13,000 a year, and student fees and books tack on another $3,000.

Those extra expenses would not be covered under Democratic Gov. Andrew Cuomo’s Excelsior Scholarship proposal, which would pay only the difference between financial aid and tuition at State University of New York or City University of New York campuses for full-time students from families earning $125,000 or less.

Students interviewed by The Associated Press said that any tuition help is welcome, but they could also use help paying for the many other costs of a college education.

“It’s less that my parents would have to pay. It’s less that I would have to pay,” said Nigel Peters, a sophomore at Buffalo State College, part of the state’s sprawling public college system, which includes 64 State University of New York and 24 City University of New York institutions.

But “enough?” he said. “No, not at all.”

The 19-year-old’s parents in Queens work overtime to keep the financial burden off of him and his twin sister, who attends college in Delaware. His mother, who already juggles positions in accounting and retail, recently picked up a third job, at an arena box office. They make too much to get aid now, he said, but “we don’t make enough so that my parents don’t have to work their behinds off to put me and my sister through school.”