Fairfax County supervisors unanimously endorsed a controversial plan yesterday to give a private developer up to 146 acres of prime public land -- valued at $50 million to $70 million -- in return for the construction of a new county government center west of Fairfax City.

By a 9-to-0 vote, the Board of Supervisors authorized County Executive J. Hamilton Lambert to advertise nationally for developers interested in jointly developing the center with the county government. It would transfer many of the county's offices from congested Fairfax City to a 183-acre tract near I-66 and Rte. 50, south of the Fair Oaks Mall.

Assuming the supervisors accept one of the developer's proposals, the new center would become yet another major feature of the Fair Oaks area, which has become one of the hottest development corridors in the Washington metropolitan area. The Detroit-based Taubman Co., which owns and operates the five-year-old Fair Oaks Mall, recently announced the addition of 25 to 50 stores to its 125-store mall, which is rapidly becoming surrounded by new office buildings.

The board's vote to seek development proposals came at a meeting during which it voted 5 to 4 to require restaurants with more than 100 seats to require nonsmoking sections.

Lambert had recommended that the county reserve 70 acres at the site for its new office complex, leaving the remaining 113 acres, plus an additional 33 acres of county land on a nearby tract at Rte. I-66 and West Ox Road, for developers.

The supervisors, however, signaled their desire to reserve 100 acres for government offices, asking Lambert to study the possibility of reducing the amount of land the county would have to trade to make its proposal viable.

"This land becomes more valuable each day," said Board Vice Chairman Martha V. Pennino (D-Centreville), arguing that if the county retained more land at the site it would be "in a better bargaining position" with developers.

Both Pennino and Supervisor Elaine N. McConnell (R-Springfield) said the county would probably need more than 70 acres to build a center large enough to handle its needs in the coming decades. Fairfax placed most of its offices in the 12-story Massey Building 16 years ago, but the rapid growth of the county has forced the government to rent office space in numerous buildings at a cost of $5 million a year.

Officials say that any exodus from Fairfax City, the county seat since 1800, is likely to be gradual and that the county courts and some offices would remain in the city.

A final decision on the land transfer and how much property to trade away could come as early as next summer, following hearings on the developers' proposals. Yesterday's vote, however, was seen as a major endorsement by the county board of the new government center, an issue the supervisors had dodged for years, fearing taxpayers would object to the estimated $70 million cost of bonds to finance the project.

Board Chairman John F. Herrity reaffirmed his distaste for such a bond issue yesterday, saying "Why would we want to go into debt and compete with roads and schools to accomplish this?"

Supervisor James M. Scott (D-Providence) echoed the enthusiasm of most supervisors, hailing the joint venture as "an enormously good investment for the county."

The only critic of the plan yesterday was Supervisor Audrey Moore (D-Annandale), who nonetheless voted to seek bids from developers. Moore said her support was contingent upon the kind of proposals that are submitted.

She called for full disclosure from any Fairfax officials involved in the project to avoid public suspicions that someone may be benefiting from it. "All of us would be willing to go nude in public as far as disclosure," shot back Herrity.

Pennino also took exception to Moore's comments, criticizing her for questioning the closed-door meetings of a board committee that preceded yesterday's proposal. "The fact that we've discussed this in private doesn't mean we're doing something behind the public's back," Pennino said.

Lambert said after the vote he saw no legal obstacles to the joint venture and cited a proposed Arlington office building that will contain both public and private offices as an example.