Azlan Guttenberg Smith of Santa Rosa, Calif., is a 17-year-old self-described book maniac with a near-perfect SAT math score. He applied to 13 colleges and, after months of waiting, was recently admitted to eight of them. Now, it's the colleges' turn to court him.

Last week, Brown University flew him to its campus to attend an open house for admitted students. Dartmouth College has been emailing him weekly bulletins, touting everything from a professor's Guggenheim Fellowship to the figure-skating team's third national title. Stanford University dispatched an English major to call him at home to see if he had "any questions." (He didn't.)

The power has shifted in the brutally competitive college-admissions race. For months, applicants have been vying for the attention of the same schools that are now bending over backward to woo them. A big part of the reason lies in a statistic called the "yield," or the ratio of admitted students who actually enroll. It is widely regarded as a key indicator of a school's appeal, closely watched by everyone from admissions directors at competing schools to potential donors and status-conscious applicants.

With the number of applications to many top colleges, both private and public, hitting record levels this year, it has become harder for even the most-experienced college-admissions officers to predict their yield rate when they mail admissions letters. Because many students are applying to a greater number of schools, top students likely have far more options come acceptance time than they did in the past.

"The frenzy this year seems to be heightened to a level that may make their decision-making more of a last-minute phenomenon," says Lee Stetson, dean of admissions at the University of Pennsylvania in Philadelphia, which has increased the number of open-house days for admitted students this year to eight from six last year.

State schools have stepped up their efforts too. The University of North Carolina at Chapel Hill added new open-house events this year, and has begun offering travel scholarships for needy students. "We didn't want anybody to turn us down because they couldn't afford to see the place for themselves," says Stephen Farmer, director of undergraduate admissions.

In the past couple of months, Ohio State University's admissions office has increased its staff dispatches to prospective students, treating them to such things as bagel breakfasts and pizza lunches at their high schools. "I also have more counselors taking families out to dinner than ever before," adds Mabel Freeman, assistant vice president for undergraduate admissions. The efforts seem to be working: The number of admitted students at the school who have already paid their acceptance fees is up 4 percent from this time last year.

As some schools expand their outreach efforts, others are seeing more students flock to already existing programs. Georgetown University holds four open houses a year -- two-day visits that take place largely in the spring. This past weekend produced a record number of 448 students, plus their parents, for the final open house of the year. That's about 150 students more than what the Washington campus typically considers its limit.

At Bates College in Maine, about 200 students visited the campus on one of three "reception" days this month -- double the number of visitors last year, says Wylie Mitchell, dean of admissions. Cornell University in Ithaca, N.Y., reports 1,836 student visitors to this year's 12-day open house -- over 200 more visitors to campus this year than last.

New York's Columbia University, meanwhile, says it has increased the number of "yield initiatives" this year -- from stepping up the number of off-campus receptions to adding online chat rooms for admitted students, says Jessica Marinaccio, executive director of the undergraduate admissions office.

While students tend to use objective criteria when deciding where to apply, "they often fall back on more emotional affiliations" when deciding where to enroll, says Andrew Fairbanks, a former associate dean of admission at Wesleyan University in Connecticut. That is why admissions officers keep their fingers crossed that their campus doesn't get hit with bad publicity in April -- such as the rape accusations now hitting Duke University -- and pray for sunny weather when prospective students visit.

Often, that weekend visit can make the difference. Mariah Erlick, a student in Willits, Calif., was deciding between Brandeis University in Massachusetts and Brown University. By the end of her visit to Brown last week, she felt sure that was where she would attend. "I know I'll get a great education here," she says, seated in a class on quantum mechanics.

Tommy Gamba, a Jacksonville, Fla., student with a keen interest in acting, says he has been "wined and dined" in recent weeks by the schools to which he has been admitted, which include Duke in Durham, N.C., which treated him to an elaborate dinner at a yacht club near his home, and Northwestern University near Chicago. Other schools he visited with his dad include the University of Virginia and Vanderbilt University in Tennessee.

After coming home from a long weekend of visiting these campuses, he says he was most impressed with Duke. "They gave me a bag, when I walked in, to put my papers in," he says. "You got pens for study abroad, for the Duke security program, little accessories, and there were tables set up for each (academic) department." He also recalls being impressed with a professor who remembered the name of all the students in her class.

For his part, Mr. Smith, who went on to visit Dartmouth in Hanover, N.H., after Brown flew him to Providence, R.I., last week, is trying to keep his head above the marketing and come-ons. "I've done really well at tuning it out," he says. Instead of spending too much time at the prearranged events, he is instead talking to students -- purposefully seeking out the ones who haven't been dispatched by admissions officers -- and sitting in on classes.

Last Tuesday, Brown kicked off "A Day on College Hill," a two-day open house packed with events for students, ranging from panel discussions on financial aid to a preview of campus nightlife. Mr. Smith sat impatiently through the speeches and grandstanding by everyone from the admissions dean to the university president to the mayor of Providence.

"You are the smartest, the cutest, the savviest, most dynamic, extraordinary -- I could go on and on," the president, Ruth Simmons, told the crowd. "But this is the best group of students ever admitted to Brown."