(Reuters) - Stanford University raised $1.035 billion in charitable contributions in 2012, far outstripping other schools and breaking an important threshold, even as giving remained almost stagnant nationally, a survey showed on Wednesday.

The total haul for the nation's non-profit and public colleges and universities was $31 billion, according to the survey by the Council for Aid to Education.

The top 10 fund-raisers together collected more than $5 billion, with Harvard raising $650 million, Yale $544 million, the University of Southern California $492 million and New York City's Columbia University $490 million, the report showed.

Overall, charitable contributions to U.S. colleges and universities rose 2.3 percent from 2011 to 2012, slightly more than the rate of inflation. Adjusting for inflation, total giving was virtually unchanged, inching up just 0.2 percent.

The total remained below the historical high of $31.6 billion reached in 2008 before the financial crisis cut sharply into giving.

The survey showed data from more than 1,000 non-profit and public institutions.

(Reporting by Eric M. Johnson.; Editing by Cynthia Johnston and Andre Grenon)