A Denver-based cable television firm yesterday became the third major company to announce it will not seek a cable franchise in Fairfax County because of what it called unacceptable demands by the county government.

United Cable Television Corp., which until a few days ago had been preparing to submit a bid this week, said the county had rendered its franchise, often described as one of the most lucrative in the country, of questionable value.

"It was a cold-cut business decision," said Walter S. Boone Jr., one of the local investors who had joined with United. "Frankly, the return on the tremendous investment was just on the risky side."

Applications for the county monopoly, which a study last year estimated would be worth $260 million in 15 years, are due on Thursday afternoon. County officials said they do not know how many firms will bid, although at least three others have expressed public interest.

Two other companies, Warner/Amex and Storer Broadcasting, announced earlier that they would not compete for the Fairfax franchise. Both complained about the county demands, including the amount of information on the companies' investors that Fairfax was demanding in an effort to avoid any appearance of influence-peddling in the franchise award.

Deputy County Executive Richard King said yesterday that Fairfax had used a different format but had not demanded more information than many other governments have required. Some supervisors, including Thomas M. Davis III and Board Chairman John F. Herrity, have accused the county of discouraging firms with long delays. The county took three years to develop its cable television law.

Supervisor Martha V. Pennino said the county needed the time to develop regulations that would protect the county. "If they don't want to play by our rules, they can go and put their cable systems somewhere else," she said.

Boone said yesterday the disclosure requirements were a problem, since United would have been reluctant as a publicly traded company to release the names of its major stockholders. But Boone said United had about 20 problems with the county demands, no one of which stood out.

The company also criticized the county in a letter of withdrawal delivered to Fairfax officials yesterday afternoon, signed by attorney Grayson P. Hanes, a partner in the prominent law firm of Hazel, Beckhorn and Hanes.

"United believes that construction of the Fairfax system would be a difficult and complex task under the best of circumstances," Hanes wrote. ". . . When the many requirements, regulations, and exactions imposed by the county in the RFP Request for proposal are thrown into the balance, this venture becomes an unacceptable risk."