The twin announcements threw a sharp curve into the contest, leaving Cornell’s $2 billion proposal for Roosevelt Island as the clear front-runner for what is seen as a prime opportunity to help reinvent higher education. The city is expected to select among the four remaining applicants in January, and bestow up to $400 million in land and infrastructure improvements. Mayor Michael R. Bloomberg proposed the competition last year to replicate the experience of Stanford or M.I.T. — a top-notch engineering and computer science school whose graduates could seed the region with new high-tech businesses — and with M.I.T. opting not to participate, Stanford was at first seen as the one to beat. But being a continent away in Palo Alto, Calif., took its toll on Stanford, according to people briefed on the process, who insisted on anonymity to discuss matters they were not authorized to make public. The university, with no experience building in New York, recoiled at meeting terms laid down by the city after its proposal was submitted, while Cornell, with extensive experience in the city — its medical school is in Manhattan — expected such negotiations. And even before the $350 million gift, Cornell, with far more alumni rooted in New York, was more aggressive about generating enthusiasm and financial pledges. (Mayoral aides told reporters that Mr. Bloomberg was not the donor.) In fact, all sides said that Cornell, which bluntly called the project crucial to the Ithaca-based university’s future, simply behaved as if it needed and wanted the prize more. Cornell was more willing to accommodate the city’s demands and got an earlier start raising money, and while John L. Hennessy, Stanford’s president, was personally engaged, city officials said they never had the sense that he had behind him the kind of united front presented by Dr. David J. Skorton, Cornell’s president, and its trustees, deans, faculty members and alumni. “Stanford could not or would not keep up,” said a city official who was involved. Stanford’s decision to bow out, made Friday morning by Mr. Hennessy and his board of trustees, surprised city officials and those at competing colleges. A university spokeswoman, Lisa Lapin, said Stanford’s negotiating team was still in talks with the city on Thursday, and was still in New York on Friday, when Mr. Hennessy called Mr. Bloomberg and his deputy for economic development, Robert K. Steel, to call it quits. “We were looking forward to an innovative partnership with the city of New York, and we are sorry that together we could not find a way to realize our mutual goals,” Mr. Hennessy said in a statement sent to reporters and Stanford alumni about 2 p.m. Friday. Seven institutions applied by the October deadline, and the city said no thanks to two. Besides Cornell, the three remaining contenders are Columbia University, which has declined the city’s offer of free land and instead wants to devote part of its West Harlem expansion to an applied sciences school; Carnegie Mellon University, whose proposal is for a parcel the city offered in the Brooklyn Navy Yard; and a consortium led by New York University and focused on real estate the city had not offered, a building in Downtown Brooklyn. Mr. Bloomberg has said he could choose two schools rather than one. But the city has made clear that it favors more prestigious schools and more ambitious proposals. Officials would not release the actual proposals, but Cornell, which would run its school in partnership with Technion-Israel Institute of Technology, has plans for about two million square feet, roughly double the size of Columbia’s, which is in turn much larger than the others’. Julie Wood, deputy press secretary for the mayor, said in an e-mail that each remaining contender “has a game-changing project queued up.” Reacting to the news, Councilwoman Jessica Lappin and Assemblyman Micah Kellner, who represent Roosevelt Island, called on the city to choose Cornell. Cornell officials declined to respond directly to Stanford’s withdrawal. Instead, it dropped its own bombshell with the record gift, with Dr. Skorton saying in a statement that “our entire community has come together, in a way that happens only so often in an institution’s history, with winning ideas, energy and the creativity that the mayor’s challenge deserves.” Several people involved in the process said Stanford had been surprised by the way the city handled it. It is standard practice in New York that once proposals are submitted for a building project, officials negotiate with the bidders in hopes of sweetening their offers before selecting one. So, for example, the city asked the schools to commit to a set of construction milestones, with financial penalties for failure to meet the deadlines. Stanford, unfamiliar with the approval and construction process in New York, objected to what it called a potentially expensive loss of flexibility. Cornell was less daunted by the prospect — and more eager to please the city. City officials said that the first phase of Cornell’s project would accommodate more students than Stanford’s, yet seemed more feasible, and that Stanford balked at matching some of what Cornell had proposed. In its request for proposals, the city said it would judge universities’ plans based in part on their expertise and realism in taking on a huge urban project, a factor that all along looked like a potential weakness for Stanford. “We listed that as a criterion and we meant it,” a city official said Friday. And while Stanford’s ability to bankroll the project was not seriously in question — the university routinely leads the nation in fund-raising — Cornell’s early start in gathering alumni pledges made an impression, as did the partnership with Technion. ]