It was a debate that the Prince George's County Council and school district chief Andre J. Hornsby had had many times: Should the district build another high school or expand existing campuses to handle as many as 9,000 additional students expected by 2006?

But when the council voted recently against the school board's plan to begin construction immediately to expand five high schools, the dispute escalated, highlighting cracks in the relationship between the top administrator of the 137,000-student district and the governing body that ultimately controls its budget.

"There seems to be some personal sparks that have been ignited," said Del. James W. Hubbard (D-Prince George's).

Those sparks became more evident late last month when Hornsby, along with an entourage of his deputies, walked out of a meeting with council members. Their departure came moments after the council voted against the school board plan and as council member Douglas J.J. Peters (D-Bowie) was in mid-sentence.

Angry council members fired off a letter to school board Chairman Beatrice P. Tignor (Upper Marlboro). "This action demonstrated great disrespect for the elected legislative body of Prince George's County and was, at best, unprofessional," wrote council Chairman Tony Knotts (D-Temple Hills) and Vice Chairman Samuel H. Dean (D-Mitchellville). ". . .We expect a prompt and appropriate response on his part."

Hornsby, in an interview last week, said he had not received the letter. When asked about council members' hurt feelings over his swift exit, he said, "When the vote is over, it's over. They knew I had to leave. They knew I had to get on a plane. I don't understand the need for an apology."

Hornsby, who took over the school system a year ago, has rankled politicians before. As superintendent of schools in Yonkers, N.Y., from August 1998 to June 2000, he publicly clashed with the mayor, who fired him despite his success in raising students' test scores.

The Prince George's County Council has its share of detractors as well. County Executive Jack B. Johnson (D) has complained that its members have overstepped their authority, and others have called them overly parochial. Hornsby is "a strong-willed person, and we're a strong-willed council," Peters acknowledged.

Peters described the relationship with Hornsby as fragile. Unlike Hornsby's predecessor, Iris T. Metts, who was accused of spending more time on politics than on running the school system, Hornsby has done little to build a rapport with the county's elected officials, Peters said.

Hornsby disagreed. He pointed out that he has met with council members whenever they've asked to talk. "In Yonkers and here, every decision I made was based on fact. It wasn't based on politics," he said. "This is not a game for me. This is a very serious business, and my decisions are based on what the needs of the organization are. I don't base those needs on individual council members' interests."

The dispute has clouded what has become one of the most pressing problems the school district is facing: It simply does not have enough room for the expected influx of high school students, the result of a demographic phenomenon known as the "baby boom echo," in which children born to baby boomers in the late 1980s and early 1990s are entering high school.

The council and school board have agreed to build one high school, but they said that won't be enough. So school board members decided it would be best to expand campuses because, they said, building another school would take too much time. Council members, however, objected to that plan and have formed a task force to study the issue further, with a decision expected by the end of September.

The delay has frustrated school officials, who argued that the problem has been studied long enough. The consequences of failing to build the additions are grave: The school district will have to spend $6.8 million on 111 additional temporary classrooms, officials said. Already, nearly 5,000 high school students throughout the county are housed in more than 190 trailers, and many campuses do not have space for new trailers, meaning that athletic fields or parking lots could be sacrificed.

"We are really faced with a space crisis, a financial crisis and a time crisis," Tignor said.

Council members said they refuse to be rushed into a decision. "Historically [school officials] are not used to public oversight," said council member Thomas E. Dernoga (D-Laurel). "And I'm not about to apologize for asking tough questions. When I ran [for the council], that's what I ran on. I said I would ask the tough questions."

What most council members call oversight, some on the panel consider meddling.

"We don't tell engineers how to run NASA. We ought not be telling a superintendent how to run schools," council member Thomas R. Hendershot (D-New Carrollton), a former school board member, told his colleagues at a recent meeting.

School board Vice Chairman Howard W. Stone Jr. (Mitchellville) agreed with Hendershot but added that conciliation from both sides is needed. "I just think we should just settle down, communicate with one another and try to overcome this issue," he said.

Andre J. Hornsby rankled politicians as superintendent of Yonkers, N.Y., schools.