Clearly shaping up in the G.O.P.'s grey mourning after was a three-cornered battle for party power. The combatants: Vice President Richard Nixon, New York Governor Nelson Rockefeller, Arizona Senator Barry Goldwater.

Goldwater Prospects. Far-out Conservative Barry Goldwater, who had campaigned faithfully for Nixon through the South, was the first to throw down the gauntlet. Said he hours after Nixon's defeat: "I want to figure in 1964--not necessarily as the top candidate. But I don't want Rockefeller in that spot." He tended to write off Nixon as an unemployed politician, figured that Nixon's defeat only strengthened Goldwater: "It's just what I've been saying. We cannot win as a dime-store copy of the opposition's platform. We offered voters insufficient choice with a me-too candidate. We must be different. My guess is that 80% of the state chairmen, the precinct committeemen, the workers think it is true. Everyone recognizes it except the party leadership."

Goldwater can count many allies, including G.O.P. state and county chairmen across the conservative South, the Southwest, and the Midwest from the Mississippi to the Rockies. Though he is weaker in the big-vote industrial states, his supporters make up in zeal for whatever they lack in numbers. During the campaign Goldwater became one of the G.O.P.'s most sought-after speakers, and many congressional candidates billed themselves as Goldwater Republicans. Most of the 23 new G.O.P Congressmen are conservatives--a fact that will help Goldwater. "If the Southern Democrats stay in coalition with us," he says, "we'll be even more conservative in action than we were in the last two Congresses."

Rockefeller Problems. If many key Republicans were piqued at Goldwater for blasting Nixon, even more were angered at Rockefeller for failing to turn the tide in make-or-break New York, where a 1956 Eisenhower plurality of 1,600,000 votes ebbed to a 1960 Nixon deficit of 400,000. "There is a feeling that the best effort was not put out here," said a top New York Republican who is no friend of Rockefeller's. "Nelson will have one helluva time getting re-elected Governor in 1962." The Rockefeller rebuttal: he had given 400 enthusiastic speeches for Nixon, campaigning so hard that he turned ashen with fatigue. Nixon himself held no grudges, believed that Rocky had gone all the way for him--at least after the famous Treaty of Fifth Avenue and the nominating convention.

Still the impression grew that Rockefeller, with an eye to 1964, had been campaigning as much for himself as for Nixon. His job was to woo independents, and he produced precious few. In September he rejected the Eisenhower-Nixon old-age medical-care plan and plumped for Kennedy's social security-based system. When asked in Geneva, N.Y. if he agreed with Nixon that U.S. prestige was at an alltime high--a key point in the debate with Kennedy--Rockefeller said: "I wouldn't make such a flat statement." When asked in New York City why he was not the candidate, Rocky said: "I figured that those who are in control of the convention had their minds made up already."

But Nixon's defeat has emboldened Rockefeller partisans, particularly in the industrial and Western states. Says San Francisco's William Brinton, a dogged Rockefeller-for-President leader in Nixon's home state: "Rockefeller can win in just those areas that Nixon lost--the big cities." Rockefeller's own problem now is to rebuild and reunite the New York organization, win over its Old Guardists (who had blocked much of his liberal program in the legislature). If he were to win big in 1962 Rockefeller might look very good indeed.

Nixon Choices. For the here and now, Dick Nixon is still very much the titular head of the G.O.P. With Dwight Eisenhower disqualified by age and inclination, middle-roading Nixon is the natural bridge between the left and right banks of his party. He intends to play the part forcefully. Said a top Nixon aide: "Dick will not permit a vacuum of leadership to develop for someone else to fill."

Nixon's problem is finding a political base from which to operate. He occupies neither a Senate seat nor a statehouse. Last week, after accepting his biggest disappointment manfully, Nixon flew off to Florida to soak up several weeks of sun and to make one of the toughest decisions of his career: what to do next. He was besieged by many private job offers. Which one he accepted would probably indicate his future political ambitions.

A university presidency would pay relatively little but give him prestige (as it did for General Eisenhower at Columbia), and a platform for Olympian comment on public affairs. Most frequently mentioned possibility: the University of Chicago, which is now casting around for a permanent chancellor.