A deeply divided Supreme Court squared off Wednesday over the future of affirmative action in college admissions, with liberals defending a university’s right to assemble racially diverse student bodies and conservatives worrying about the constitutional rights of those who are denied admission because of their race.

It is one of the court’s most important cases of the new term, with potentially landmark consequences for the use of racial preferences and for the debate over crafting the nation’s institutions of higher learning to reflect the country’s diversity.

At the end of a lengthy oral argument over admissions policies at the University of Texas, it seemed highly unlikely that a majority of the justices would announce a ringing endorsement of racial preferences.

But it also was unclear whether there were five votes willing to bar universities from considering race in their admissions processes. Such a ruling would renounce the court’s most recent affirmative action decision, in 2003, that universities could use race in a limited way to achieve a “critical mass” of diversity that benefits all students.

The decision will probably come down to Justice Anthony M. Kennedy. The longtime justice has agreed in theory that campus diversity is the kind of compelling government interest that can sometimes license an otherwise forbidden consideration of race.

An analysis of the 2011-2012 Supreme Court session, including justice voting patterns and key cases.

But he dissented in that 2003 case, Grutter v. Bollinger, and has never voted to uphold an affirmative action plan that has come before the court for review. His questions Wednesday indicated discomfort with UT’s use of race, but they were far short of the condemnations that came from the court’s other conservatives.

The University of Texas at Austin admits about 75 percent of its freshmen based on their graduation rankings from Texas high schools. For the remaining students, it uses a “holistic” evaluation that includes race as one of many factors.

A white applicant, Abigail Fisher, says those attempts to boost the number of African American and Hispanic students cost her a spot in the freshman class of 2008.

The court since 1978 has recognized that promoting diversity on the nation’s campuses allows universities to give some consideration to an applicant’s race, which normally would be unconstitutional.

On Wednesday, the court’s liberals recalled that, in the Grutter decision, the court said it expected that racial considerations would not be needed in 25 years.

“I know that time flies, but only nine of those years have passed,” Justice Stephen G. Breyer said.

What has changed, though, is the court’s composition. The 5 to 4 Grutter decision was written by Justice Sandra Day O’Connor, who has been replaced on the court by Justice Samuel A. Alito Jr. Alito has proved to be a fierce opponent of race-specific government policies.

The change was underscored when O’Connor entered the courtroom Wednesday a little after the argument began and took a seat in the front row, where retired justices normally sit to watch proceedings.

Fisher’s attorney, Bert Rein, did not ask the court to overturn Grutter. He said that UT has failed to narrowly tailor its examination of race and that it has not shown the necessity for racial considerations that Grutter demands.

UT, he said, has become one of the nation’s most diverse universities because of its policy of admitting any applicant from the top 10 percent of a Texas high school’s class, a policy that yields a diverse crop of students because the schools often are dominated by one race.

In filling the rest of its class, “race should have been a last resort,” Rein said. Instead, “it was a first resort.”

Justice Sonia Sotomayor was Rein’s most relentless questioner. “So you don’t want to overrule Grutter, you just want to gut it,” she told the lawyer.

Justice Ruth Bader Ginsburg said the use of race by UT — which considers it as one of many factors along with essays, leadership qualities, work experience and other characteristics — is “more modest” than what the court approved from the University of Michigan Law School in Grutter.

Kennedy told Rein that his argument that UT’s holistic policy admitted few minorities made him wonder, “If it’s so few, then what’s the problem?”

But then Kennedy said that perhaps it has such a limited impact, it might not be worth the “hurt” of considering race.

When Washington lawyer Gregory G. Garre rose to defend UT’s plan, he was pounded by conservatives, led by Chief Justice John G. Roberts Jr.

Roberts, who in past opinions has decried the “sordid business” of categorizing Americans by race, asked Garre what racial box someone who is one-quarter Hispanic, or one-eighth Hispanic, should check.

He seemed unsatisfied by Garre’s answer that all racial classifications are selected by the applicant. He suggested that the university was playing down its reliance on race, saying it was the only characteristic noted on the front of an applicant’s file. And Roberts expressed frustration with how the court was supposed to come up with a standard for the “critical mass” of diversity that Grutter said justified the use of race.

When Garre said the university could not set percentage goals — because that would run afoul of the court’s prohibition of quotas — Roberts pressed.

The court must determine whether UT’s use of race is narrowly tailored to attain a critical mass of minority students, Roberts said, “but you won’t tell me what the critical mass is. How am I supposed to do the job that our precedents say I should do?”

Alito was scornful of UT’s argument that the holistic approach allows it to achieve “diversity within diversity.” The school in its brief used as an example its desire to admit a black or Hispanic child whose parents had professional careers but who had not made the top 10 percent in a competitive high school.

“I thought the whole purpose of affirmative action was to help the disadvantaged,” Alito said. He asked why a minority child of the “1 percent” should get a “leg up against, let’s say, an Asian or a white applicant whose parents are absolutely average in terms of education and income?”

Garre said the university recruits minorities from all walks of life, prompting Kennedy to tell him: “What you’re saying is race counts above all.”

Garre also said Fisher should not be able to bring the suit because she did not have the qualifications to make it into the 2008 freshman class regardless of her race. She graduated from Louisiana State University last spring and now works in Austin.

The case was heard before only eight justices. Justice Elena Kagan recused herself, presumably because she worked on it as President Obama’s solicitor general.

Her successor, Donald B. Verrilli Jr., told the court that it should uphold UT’s plan and that making sure the nation’s top universities produce diverse leaders is a “vital interest” of the United States.

One option for the justices is to rule narrowly on UT’s process — for instance, to say its holistic approach using race is not necessary because of its top 10 percent policy.

If the eight justices deadlock on a decision, the school’s policy would remain in place without setting a precedent.