NEW YORK, May 2--On a day in which there were literally hundreds of meetings on the Columbia campus, many students turned from the demand that the president must go to the larger point that, in effect, the presidency must go.

At meeting after meeting, students spoke of the need to "restructure this university so it is run by the students and faculty."

It was a strong form of the old and boring "student power" issue, but well over a thousand students yesterday were taking it seriously.

The speeches took place primarily in meetings of "communes"--groups of 70 or more students who banded together for the purpose of electing a delegate to represent them at the Strike Steering Committee. Communes met in buildings or on the lawn.

The typical proponent of "restructuring" sympathized with SDS causes but wasn't a SDS member. He probably did not sit in, but was the victim of police pelting anyway.

Most of the enthusiasm was not translated into specific plans for operating the university without an administration, or with a very weak one. But one member of the SDS steering committee, Ed Hyman, outlined a plan which he said he will soon present to the students.

Hyman wants a tripartite commission of students, faculty, and local residents to handle Columbia relations with the community; a tripartite commission of students, faculty, and workers to over-see the university's labor policy; and a bipartite commission of students and faculty to take care of academic matters.

Hyman's plan, which would leave the administration menial tasks, is not likely to be well received by the faculty. Several hundred faculty members appear willing to see Kirk leave, but many express their faith in David B. Truman, university vice-president and Kirk's heir apparent.

Columbia's president and board of trustees theoretically play about the same role as Harvard's president and governing board. Columbia's administration exerts greater influence in educational matters than its Harvard counterpart, which leaves such problems to its faculty.