When Stanford law professor William F. Baxter appeared at his confirmation hearing as the Reagan administration's top antitrust cop last March, he said that the job was the one government position he'd always wanted to tackle.

Now, after less than a year in office, he has alternately delighted and outraged his constituency in corporate boardrooms, the private antitrust bar and the Congress. And he's advertised a comprehensive program to remove restrictions he feels have hampered the competitiveness of American industry.

In the face of opposition from Cabinet secretaries at Defense and Commerce last spring, he promised to litigate the giant American Telephone and Telegraph Co. case "to the eyeballs." Then last month while on a ski trip to Utah he signed a settlement agreement that will reshape the nation's telecommunications industry.

E. William Barnett, of Houston, head of the American Bar Association's antitrust section, calls the 52-year-old Baxter "a breath of fresh air" and claims Baxter has sharply defined the most basic questions about what the antitrust laws are all about.

Sen. Howard Metzenbaum (D-Ohio), a defender of the populist school of antitrust enforcement, sees it differently. He told Baxter at a hearing last fall that he felt he was breaking the law by not following court precedents with which he disagreed.

Metzenbaum and a few others also have expressed concern about possible conflicts of interest stemming from the professor's work for corporations ranging from Northrop to Visa to the American Petroleum Institute. API asked him to examine and testify in 1979 on a proposed bill to bar large mergers by major oil companies.

Baxter has agreed to stay out of cases involving a few former clients.

The long-time scholar turned bureaucrat has an irreverent attitude that is seen in the titles of some of his scholarly works: "People or Penguins, An Optimum Level of Pollution," and "The SST: From Watts to Harlem in Two Hours." And when a visitor commented during an interview that at least the stopped clock on his office showed the correct time twice a day, he replied, "Not bad for this town."

Some observers of the bureaucratic battlegrounds of Washington say the same about Baxter's performance in getting the AT&T case to settlement at all, over the objections of Secretary of Defense Caspar Weinberger and Secretary of Commerce Malcolm Baldrige.

Weinberger was worried about the Bell System's key role in national security communications. Baldrige felt the case was holding up consideration of a rewrite of the 1934 Communications Act.

Attorney General William French Smith and his deputy, Edward C. Schmults, had to excuse themselves from the case, so Baxter was the equivalent of a colonel facing a couple of four-star generals who wanted him to drop a pet project.

One participant in the White House discussions about telecommunications policy said the Reagan team was following an argument prepared by the Carter administration: that the AT&T case was hurting the chances of legislative reform. The Justice Department wasn't even invited to participate at first.

"We had the case. We were seen as part of the problem, not the solution," one Justice official said.

Another said that Jonathan Rose, assistant attorney general for legal policy, carried a counter argument to the White House last summer, arguing that killing the case would have the opposite reaction in Congress and doom a rewrite of the communications act.

Bernard Wunder, assistant secretary of Commerce for communications and information, said his task force staff had recommended dropping the case because the communications industry needed the certainty of new legislation, and the suit threatened to drag on for years. He recalled that much of the internal disagreement was settled when Baxter agreed to drop the case if Congress wrote a bill he could live with.

Then, last September U.S. District Court Judge Harold Greene ruled that the government had presented strong evidence that AT&T had violated the antitrust laws. "His opinion laid out the case for people," one administration official said. "From then on, we moved on both tracks, the legislation and the settlement talks."

Lawrence Sullivan, a law professor at the University of California at Berkeley, said he couldn't help wondering about the depth of the internal administration objections to the case. He noted that Commerce and Defense acquiesced in the settlement as soon as AT&T Chairman Charles Brown dropped around to explain it in person.

"They went to sleep on these issues as soon as AT&T said it was okay. That suggests that their analysis of the issues was more a reaction to the industry position than an internal government one," he said.

Not everyone is happy with the outcome. Sen. Harrison Schmitt (R-N.M.) attacked Baxter Thursday at a communications conference for being "so extraordinarily self-centered" he ignored the Senate's views in his AT&T settlement.

Some of Baxter's employes say they have felt ignored too, by his aloof manner. The division's last boss was Sanford Litvack, a gregarious litigator. Baxter, by contrast, has been described as enigmatic and arrogant. Some lawyers report morale is low; others complain that for all his talk of "economic efficiency" he's not a very good manager. They wonder if his performance will match his phrasemaking.

Baxter has three grown children from a marriage that ended in divorce. He lives now with Carol Treanor, a computer expert for the American Enterprise Institute, and her 11-year-old son Bernard.