ALBANY — The idea is dubbed “making college tuition free,” but the number of students who qualify will be limited. Further, New York’s newest higher education initiative includes some conditions in the fine print that could curb its appeal for some.

Here’s what you need to know about what Gov. Andrew M. Cuomo and lawmakers are calling the “Excelsior Scholarship,” which will provide a pathway to a tuition-free education for some students at the City University of New York and State University of New York campuses.

The idea started at community colleges in other states and gained national attention in Sen. Bernie Sanders’ presidential campaign.

Minnesota, Oregon and Tennessee have made their community colleges (two-year) tuition-free. Tennessee’s is often referred to as the most successful model to date.

Cuomo, who some believe is trying position himself nationally, held a news conference with Sanders in January in Queens to kick off his push for the idea in New York. Cuomo is expected to return to LaGuardia Community College to have a bill-signing ceremony Wednesday.

New York becomes the largest state to offer a path to tuition-free college for some at its four-year colleges. The program also includes two-year community colleges such as Nassau Community College and Suffolk County Community College.

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New York already had a financial-aid program that covered tuition for the lowest-income brackets.

Generally, if a student’s family earns $50,000 or less, his or her tuition costs can be covered entirely by the state’s long-established Tuition Assistance Program and federal Pell grants. The new “Excelsior Scholarship” instead helps families earning roughly $50,000 to $125,000 annually.

Importantly, Excelsior will be what’s known as a “last dollar” program. That means a student must first apply for TAP and Pell help before applying for whatever amount remains to be covered.

The income limit is increased over several years: $100,000 in fall 2017, $110,000 in fall 2018 and $125,000 in fall 2019.

Students must earn 30 credits per year and graduate in four years.

For some, this might be the most daunting of the “strings attached” to the Excelsior Scholarship — especially when the national four-year graduation rate is running around 34 percent.

And it is tougher than TAP conditions, which mandate 12 credits per semester and can be used across five years.

The Cuomo administration acknowledges it wants to provide an incentive for students to finish faster and, therefore, accumulate less debt.

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Recipients must agree to live and work in New York for four years after graduation. If not, the scholarship converts to a loan – which must be repaid.

This is the second big condition that critics say might limit participation.

“Why should New Yorkers pay for your college education and then you take off and you move to California?” Cuomo reportedly said Monday. “If you don’t stay here, then go to California and let them pay for your college education.”

But Sara Goldrick-Rab, a Temple University professor and high-profile advocate of tuition-free college, took to Twitter to call this condition a “trick” that would cause some students to decline the offer.

The Cuomo administration said more than 80 percent of CUNY and SUNY graduates already stay in New York and said the provision was meant to prevent someone from moving here for a brief while to take advantage of the program.

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A spokesman for Senate Majority Leader John Flanagan (R-East Northport) acknowledged Republicans insisted on the residency requirement.

It doesn’t cover room and board, fees and books – which account for more than half of students’ costs.

SUNY tuition currently is $6,470 while a student’s total expenses run upward of $20,000. So even if he or she doesn’t pay tuition, it doesn’t mean college is free.

The state is hiking tuition for everyone else.

Cuomo and lawmakers will hike SUNY tuition $200 per year for the next three years.

Total participation likely will be less than you first think.

Cuomo has said that some 940,000 New York families are eligible to participate. But the administration has said a more realistic figure is a 22,000 bump in enrollment the first year and 32,000 by fall 2019. SUNY currently has about 440,000 full-time students.

Assemb. James Skoufis (D-Orange County), who wanted a broader program, says the projections might be a stretch, given the participation requirements. “SUNY and CUNY is not becoming ‘tuition free’ for the vast majority,” he said.

Cuomo is claiming a political win and touting the initiative nationally.

“We have the nation’s first accessible public college program, which is a national first,” the governor said.

Since the election of President Donald Trump, Cuomo has sought to speak out more on issues important to Democrats and, notably, make his case that government can work to help people. “You want to talk about a difference government can make?” the governor said of his tuition program. “This is the difference that government can make.”