State aid to public universities has been falling, now accounting for just 25 percent of the budget at the University of Wisconsin, 13 percent at the University of Virginia and a bare 10 percent at the University of Michigan. That's prompting universities to ask for more independence from state governments, which often control everything from staff salaries to tuition. And although a complete break with state funding is not what the state schools have in mind, there's widespread talk of ''privatizing'' public colleges.

In a move that many public colleges are watching closely, Miami University in Oxford, Ohio, recently said it will begin charging $16,300 in tuition for in-state and out-of-state students alike. Miami will use its state aid to give Ohio students an automatic $5,000 yearly ''residency'' scholarship. But that still leaves Ohioans with a $3,700 fee increase that the university says it will use to compete with private schools by recruiting the best students, keeping class sizes small and raising salaries to attract the best teachers.

The University of Virginia's law and business schools will become self-supporting by next year, using tuition and privately raised money to fund all of their operations, and even returning 10 percent of their tuition income to the university for operating costs like heat, security and accounting services. The university talks of moving toward the same arrangement with its medical and undergraduate business schools.

The University of Texas is lobbying the state Legislature for authority to set its own tuition, including charging more for highly sought programs like advanced business degrees and less for programs like social work where potential salaries are low, and even offering a discount for late-afternoon classes. With tuition capped at $4,000 and the state providing just 22 percent of the budget, the chancellor, Mark Yudolf, says the nine-campus university can't compete with the private schools that it sees as its academic equals. ''We're much like a Russian grocery store: long lines, low prices and not much food,'' he says.

In some cases, it's the state, not the schools, pushing for more market-oriented solutions. Legislation before the Colorado House of Representatives would drop the yearly appropriation the state now gives its 28 public colleges. Instead, Colorado would offer vouchers of $4,000 each to in-state students to use toward tuition at any of the schools. Backers say the proposal would force colleges to compete and specialize.

College presidents and others who talk about these as the first steps toward ''privatizing'' the public universities concede that's not exactly what they mean. No one wants to give up state aid, which was $56 billion nationally in 2000 and amounts to more than $1.5 billion at the University of Texas alone. Most universities also depend on their states to pay for classrooms and other infrastructure. ''We have not come up with the right word for it yet,'' says Leonard Sandridge, the University of Virginia's chief operating officer.

Whatever they're called, the moves are prompted by a long-running shift in state priorities. The states' financial support for their colleges has almost tripled in the past two decades. But because university budgets have grown even faster, state aid accounted for 36 percent of university budgets nationwide in 2000, down from 46 percent in 1980, the U.S. Department of Education says. That trend isn't likely to turn around: Most states have ballooning Medicaid and elementary and secondary-school expenses. But beyond that, they're also deciding that students should pay more because it will vastly increase their earning power.

The University of Michigan made the first moves toward independence in the early 1980s after it had lost about a third of its state support in a recession. The university increased its out-of-state enrollment and began charging those students what they would pay at its private-school competitors.

The new financing arrangements often give universities new control over purchasing, payroll and other functions that many states now perform.

Public universities say they need sharply higher tuition to compete with private colleges, which, according to the Chronicle of Higher Education, pay their faculty members an average $22,000 more per year. Good teachers attract good students, but they also attract research grants, which in turn help finance new labs and buildings.

Record demand for college admission over the next decade means that universities with strong reputations may face little opposition to big tuition increases. James Garland, Miami University's president, says that applications are up 27 percent this year, and that more than a quarter of Miami students already come from out of state, paying tuition that's not much less than what's charged at such well-regarded private colleges as Rice and Stetson universities. In the upside-down world of college tuition, moreover, low price is often equated with low quality: Miami expects that boosting tuition will actually attract more Ohio students.

Of course, not every university has the market pull of Michigan or Virginia, or even of Miami University, which likes to think of itself as a ''public ivy.'' Many smaller public colleges lack the reputation to attract research grants or high-paying students, and depend on their states for crucial support. And even some nationally famous universities find it isn't always easy to work out new financial arrangements with their states. Four years ago, the University of Wisconsin at Madison persuaded the state to match any private money the university raised. It planned to use the new funds to expand research and in the process boost revenue. But after two years, the state stopped providing the matching funds because of its own budget problems. Private donations dried up when the state money ended. Now, the state also plans to cut yearly aid to the Madison campus by $20 million.