University of North Carolina officials have hired the law firm of Fulbright and Jaworski to defend the state's higher education system in a dispute government over college desegregation.

Officials of the Department of Health, Education and Welfare and the state are trying to reach an agreement on a five-year desegregation plan for the state's 16 four-year colleges and universities.

Meanwhile, the state has hired Carl Vogt of the firm, whose partner is former Watergate special prosecutor Leon Jaworski, to prepare the case. "We don't want to be caught unprepared" if the matter goes to court, a university spokesman said yesterday. Founding partner (R. Clarence Pulbright died in 1940.)

The governing board of the state's university system is to decide later this month whether to take the matter to court.

HEW wants the state to further desegreagate its 16 senior colleges and universities or lose federal funding. Blacks represent 8.8 per cent of the student population at the 11 predominantly white institutions. Whites compose 8.4 per cent of the student population at the predominantly black colleges.

North Carolina is the only one of six southern states that has failed to present an acceptable college desegregation plan to HEW in complance with a court order.