Price George's County Executive Lawrence J. Hogan this week ended a three-year battle with the County Council and signed into law a bill that sets county-owned hospitals free.

The hospitals will be run by a nonprofit corporation, with the county paying for services to the poor but having no control over management.

The 555-bed Prince George's General Hospital in Cheverly, the half-empty, 236-bed Greater Laurel-Beltsville Hospital and the Bowie Health Clinic, which handles about 35 patients a day, are now run as a government department.

Under the new plan, the council will create a 15-member board of directors composed primarily of county residents chosen in consultation with community and professional groups, and will include representatives of business, medical and consumer interests. This board's first task will be to look for a top-level administrator.

Once this is accomplished, a lease will be drawn up outlining the responsiblities of the new corporation, which will be signed by the county executive and corporation officials, and the hospitals will then be tranferred from the county government to the corporation.

"The change will be transparent to the patients and employes, in my opinion," said hospitals director Richard Iannucci. But hospital officials agree that administrators, able for the first time to run their institutions without constantly seeking approval from top county offices in Upper Marlboro, will find it easier to operate the hospitals efficiently.

Hogan fought hard for three years to lease the institutions to the profit-making Hospital Corporation of America (HCA), but his plan was rejected by the County Council last October. Some council members opposed provisions in the lease that would ban abortions in Prince George's hospitals and others objected to what they saw as inadequate financial protection for the county.

Last January, a hospital committee was set up by the council, headed by council member Ann Lombardi, who was Hogan's fiercest opponent over the HCA lease. Lombardi's committee recommended that hospitals be leased to a nonprofit corporation created by the county.Over Hogan's objection, the council unanimously supported it last month.

Hogan may have lost a philosophical battle but even some of his opponents acknowledge he forced the County Council to come finally to grips with the decade-old problems of a large and troublesome hospital system.

Although Hogan and the council still don't agree on whether the HCA lease or the nonprofit corporation makes more sense financially, neither side disputes the real gains of removing the hospitals from the direct authority of the county government. Among them:

* Appointments: Constant battles between the executive and the council have left administrative positions unfilled, sometimes for years. The only time all positions on the Hospitals Commission, and the board of directors for each of the three hospitals, which operate under it, were filled was at the beginning of former executive Winfield Kelly's term, in 1975.

Until eight new directors were appointed last week, the Bowie Health Center had been operating for almost two years with only four of its allotted 13 directors because of disputes over who should fill the positions. The boards of directors of the individual hospitals make budget recommendations and work out priorities within their allotted budgets. But because Bowie had too few board members to muster a quorum, every decision had to be made again by the Hospitals Commission, which makes overall policy decisions for the hospitals.

Iannucci, who was appointed director of the hospitals last week after six months as acting director, complained that politics had played too great a part in disputes over appointments -- including his own. Before coming to the county, he was on the staff of the Air Force surgeon general. "I helped manage 130 Air Force medical facilities." he said. "People keep saying I'm a Hogan man. Nobody recognizes that I have the credentials."

Under the nonprofit corporation plan, appointments will be approved by a self-perpetuating board of directors, rather than the county executive and council, and that should end such squabbles.

* Staffing: Hospital administrators are now largely at the mercy of the county government when it comes to staffing policy. When Hogan took office in 1979, for example, he tried to control county spending by establishing rigid procedures for monitoring everything from hiring and overtime to printing costs and gas mileage. Nurses at Prince George's General, where there was a 40 percent annual staff turnover, complained that strict hiring review procedures amounted to a hiring freeze.

Royal Hart, the former County Council member and current council assistant working on the nonprofit hospital corporation project, said one county hospital lab was closed for three days last year because the county government was trying to reduce staff overtime.

* Building management and purchasing: Any request for nonmedial purchases by the county hospitals that will cost more than $4,000 must be sent to the county and offered out on a contract basis. Iannucci said the system "is not as responsive to our needs as a hospital our size is accustomed to;... any time you want equipment you are anxious to get it."

Lombardi recalls a leaking roof that took 11 months to repair because hospital officials were forced to go through three levels of county government before reaching the contractor.

Bowie Health Center administrator Dennis McDowell complained that there are "many layers of delay and decision-making, and a lack of a clear locus of responsibility." The new hospital corporation promises "big freedom, big improvement," he said.

* Data Processing: The county hospitals want their own computer system, to provide minute-by-minute analyses of such things as precise nursng requirements and inventories. The county's computer in Upper Marlboro cannot perform many tasks the hospitals require, and the hospital system can only use it late at night. A county consultant recommended a separate computer system for the hospitals six years ago.

The lingering question of whether the nonprofit corporation could make enough money to survive was at least partially answered last month when Iannucci announced that the hospital system had made $3.36 million between February and May, after losing $2.9 million during the previous six months, and said he would not need any county money to run the hospitals for the following year.

Last November, Hogan told the County Council it would "find that the Hospitals Commission's fiscal woes are beyond the ability of the county or a county-supported hospital authority to solve."

Iannucci credits the apparent financial turnaround to a special management team he set up when he took over as acting director in January. Inventories were reduced, he said, and overtime and hirings were cut in areas not directly involving patient care.

Lombardi said the figures lent more support to her long-held belief that "the system can be self-sustaining." But she added that the brighter outlook had more to do with reshuffling often-confusing financial figures, work done by Iannucci's predecessor, hospital rate increases and the "ebb and flow" of patient admissions.

Indeed, after averaging a $580,000-a-month income from February to May, Prince George's General's earnings slipped to $158,458 in June. Iannucci said the drop occurred because the hospital had "deferred so many purchases" earlier in the year, and predicted the situation would not improve until the fall. Still, Iannucci said June's earnings were better than the $463.573 loss the hospital suffered in June 1981.

Despite these differences of opinion, however, the creation of a nonprofit corporation offers relief from the difficulties the hospitals have faced. "There are questions of how things will shake down," said Bowie administrator McDowell. "But most people think this is an opportunity to resolve most of these problems."