Fairfax County's tax coffers are overflowing, and county taxpayers are about to share the bounty.

For months, new buildings have been rising around the county and car sales have been soaring as the economic recovery swept Northern Virginia with a vengeance. The result was astounding to those accustomed to reading the unending stories of budgetary deficits in Washington: Fairfax was running a fat surplus.

With the county's coffers brimming, the talk of the county board is of tax cuts. And the supervisors, who make the final decision on the real estate tax rate, are asking not if they should cut, but by how much.

"I want to see a meaningful tax cut," said Republican Supervisor Nancy K. Falck of Dranesville district this week, hinting that she will support lopping a nickel or more off the current real estate rate. It stands at $1.46 per $100 of assessed value -- the highest in Northern Virginia.

"We can probably go closer" to 10 cents, said Democrat Audrey Moore of Annandale. She said she would like to see county taxes cut on both real estate and personal property, primarily automobiles, trucks and boats.

Monday the supervisors learned that the county had a surplus of about $19 million at the end of the third quarter of the current year. Even after $6.6 million is earmarked to pay for the county's asbestos cleanup program and other projects, Fairfax will be left with a surplus of $12.3 million.

For fiscal 1986, County Executive J. Hamilton Lambert has proposed a balanced budget with no tax rate change.

Each penny the supervisors want to trim from the real estate tax rate equals a loss of about $3 million in revenue. That means that, should the board decide to knock a nickel off the tax rate, it must come up with $15 million in surplus funds, budget cuts or new revenues.

The board is scheduled to vote on a new budget and set the fiscal 1986 tax rate April 15 after a series of public hearings next week.

One caveat for county taxpayers: even if the county board votes to slash taxes, that does not necessarily mean that all Fairfax residents will be paying a lower tax bill.

The average assessment on a home in Fairfax is rising by 4.4 percent, according to the county Office of Assessments. In other words, unless the tax rate is cut by a nickel or more, the typical county taxpayer's bill will still increase.

That is a familiar trend in Fairfax. Since fiscal 1978, the real estate tax rate has fallen by 28 cents, from $1.74 to $1.46. But the actual tax bill paid by a typical household in a year has risen from $984 to $1,491 because of skyrocketing home values.

Supervisors uniformly say they want to see a "real" tax cut this year -- one that would at least offset the rise in home assessments. The only real question seems to be whether the cut will be large enough to simply freeze an average homeowner's tax bill, or actually reduce it.

The chances for a tax cut as large as a dime, such as Moore endorses, seem slight, if only because board members cringe at the idea of decreasing taxes one year only to be forced to raise them the next.

"We want to make sure we don't have to go back next year with an increase," Falck said.

When the supervisors get set to trim Lambert's budget to make room for a tax cut, one likely target will be a proposal to spend $14 million next year for preliminary work on a sprawling new governent center west of Fairfax City.

The project, which would be the largest investment ever made by the county in the proposed complex, would translate into nearly 5 cents off the tax rate if it is scrapped.

The board is not bound to building the new complex, and several supervisors have questioned the value of spending preliminary money on a project that may never be completed.

A month ago, after Lambert proposed spending $14 million on the project, Democratic Supervisor Joseph Alexander, who has favored the new government center in the past, threw up his hands.

"Where's the board going to find the money for a tax decrease?" he said.

With the surplus in hand, the board may now have a second place to look.