The Fairfax County Board of Supervisors yesterday approved legislation carving the huge county into three separate cable television franchises that should begin operations by mid-1982.

On a vote of 8 to 0 with one abstention, supervisors in Fairfax joined Arlington and Alexandria in embracing lucrative cable television systems that ultimately could generate million-dollar profits. Fairfax officials are hopeful that their cut of that profit will top $400,000 a year by the early 1990's.

Under the ordinance, adopted after the supervisors turned down a proposal to give a citizens' committee a role in the award of cable franchises, contracts for the three Fairfax systems are expected to be granted by the end of the year.

Bidding for the franchises is expected to be heated. As many as 18 cable television firms, including several national organizations, have expressed interest in writing the affluent Washington suburb in recent months. At least 13 former or current public officials have affiliated with potential bidders, raising questions of possible political pressures being brought on Fairfax supervisor.

Board chairman John F. Herrity said yesterday, however, he doubts that pressure from a state legislator, former county supervisor and others will interfere with the awarding of contracts.

"you've got to remember that on all of these companies you'll find a political enemy -- and a political friend," said Herrity, a Republican. "all of them have a Republican and a Democrat. They all cancel each other out."

If all goes according to Fairfax's plans, 20 percent of county residential units will be reached by a cable television system by the middle of 1982. An estimated 85 percent of county homes will have access to a cable system by 1986.

According to county cable adviser Archer Taylor, a member of the Washington consulting firm of Malarkey, Taylor and Associates, it is likely that cable service will be provided first to the county's most densely populated areas including Mason District, Annandale, Springfield and parts of McLean.

The ordinance provided that cable systems would be established in three separate areas of the county: the Reston area, which is already served by the Warner-Amex Cable Corp., and the northern and southern halves of the county, as bisected by the Little River Turnpike, Rte. 236. Reston service is expected to remain with Warner-Almex, although the other two areas are considered up for the grabs.

Fairfax is not the only suburban jurisdiction considering award of a cable franchise. Both Montgomery and Prince George's counties are planning to award cable franchises.