Olympic athletes work to be No. 1. Politicians strive for it. Recording artists count on it. But two Northern Virginia counties don't want the distinction.

For years, Prince William has claimed the designation of being the fastest growing county in Northern Virginia. Now come Stafford County officials waving a document from the Tayloe Murphy Institute, a research organization affiliated with the University of Virginia's graduate business school. Stafford officials say the institute's population study gives their county the honor of being the fastest growing one in Virginia's Washington suburbs.

And officials of both counties, heads spinning with the problems that come from such growth, are handing the title back and forth so fast it looks like a tennis match.

No one disputes that Prince William has more people. With a jump from 144,703 people in 1980 to an estimated 156,700 in 1982, the county claims 426 residents for each of its 339 square miles. Stafford gained an estimated 3,400 residents between 1980 and 1982 for an estimated total of 43,870 residents. That is 149 people for every one of Stafford's 271 square miles.

But percentages tell a different story, with Prince William growing at the rate of 8.3 percent annually and Stafford boasting an 8.5 percent rate of growth, according to Tayloe Murphy.

"If they want to claim the title of fastest growing county let 'em have it," said Richard Trembley, Stafford's acting planning director. "We're so concerned about the financial problems of providing services and facilities that we'd rather not be No. 1."

Although 75 percent of Stafford is agricultural, forested or open space, the Aquia-Garrisonville area in the north and the Falmouth-Chatham area to the south are attracting new residents so quickly that another elementary-middle school will soon have to be built to handle the overflow from one constructed just two years ago, Trembley said.

"We'd rather say we're the slowest growing county," said Alvin Bandy, chairman of Stafford's Board of Supervisors. "We're not the fastest growing county because we want to be; we're the fastest because of where we are."

The heart of the county is about 45 miles from the District, Trembley said, with about 80 percent of the county's workers commuting to Washington or to other parts of Northern Virginia to work. "Like it or not, we're a bedroom community for the Washington metropolitan area," he said, adding that the county is doing its best to change that by encouraging new businesses and industries to locate in Stafford through the use of tax-free industrial development bonds.

"No. 1? I don't think that's a title anyone really wants anymore," said Prince William County planner John Schofield. Still, considering the numerical versus the percentage data, "it's like comparing apples and oranges," he said. "It's all done with mirrors anyway."

According to the Tayloe Murphy Institute, Fairfax County had an estimated population of 637,800 in 1982, a jump of 42,100 from 1980. That is 1,518 people for each of Fairfax's 400 square miles. Figures for all counties do not include the independent cities within county boundaries, according to Julia Martin, who cowrote the Tayloe Murphy report.

The report, titled "Estimates of Populations of Virginia Counties and Cities," was released last year. According to Martin, such a report is done annually in cooperation with the Census Bureau in between regular census years. The data from these reports are used to determine various types of state funding.

In spite of an influx of people in recent years, neither county can claim to be the fastest growing in the state, although Trembley said he thought Stafford had that distinction as well. According to the report, Gloucester County in the Virginia Tidelands has that honor, with a 9.6 percent growth rate, jumping from 20,000 people in 1980 to an estimated 23,000 in 1982. That is 89 people for each of the county's 225 square miles.

"Pin the title on little Gloucester," Schofield said. "They can have it."

Schofield said that schools are any fast-growing county's prime concern, that good schools bring people into an area, and that keeping good schools is the first thing new residents demand.

Roads? "When you live in the Washington area you expect bad roads," said the planner, who hails from North Carolina. As for water, "as long as it flushes when you need it to and there's plenty coming out of the faucet, water is a problem for developers, not residents."

At least neither Prince William nor Stafford can claim the title of being the county with the largest loss of population since 1980. That dubious honor goes to Bath, a rural county in the Allegheny Mountains. Bath lost 600 people from 1980 to 1982, Martin said, a loss rate of 10.9 percent. That left about 5,200 people to populate Bath.

Where did they go?

"I hope they went to Stafford," said Prince William's Schofield. "We've got enough problems."