Until 6:45 yesterday morning, Terminals Unlimited Inc. was, according to Inc. magazine, the nation's fastest growing private company, a designation the Falls Church firm received just last month when another high growth computer firm left Inc.'s list by going public.

But the Inc. tabulation changed again yesterday when Terminals Unlimited's chief executive, David Owens agreed at that early hour to sell his company to Duke of Energy Corp., a Cushing, Okla., firm that hopes to put together a $1 billion computer services company within three years. Its headquarters will move to Dallas Jan. 3.

For Owens, a one-time computer equipment salesman who started Terminals six years ago with $1,000 in savings, the sale represents a substantial corporate and personal nest-egg, since he holds 98.5 percent of Terminals' stock. The purchase price was 3.52 million shares of Duke of Energy's over-the-counter stock -- a package, at current value, worth more than $21 million.

However, it was more than personal gain, Owens said, that put Terminals Unlimited into a position where it either had to be taken over or move into the equity market.

"When you do something like this, it's almost like giving up a child, but one of the problems you have as a growth company is that there is a continuous financing problem," Owens said in an interview.

So far, that problem doesn't seem to have stunted the growth of Terminals Unlimited, which sells printers, terminals, data communications gear, computer systems and software and service, although it does little manufacturing at the present time. Its sales this year will be about $21 million, up from 1981 sales of $16.7 million, and the company reports an annual compounded growth rate of about 212 percent over the past five years. Owens predicts 1983 sales of about $50 million

Private companies are responsible for about 60 percent of Terminals Unlimited sales and the customers include major computer concerns like American Management Systems and CACI Inc. In addition, the company signed an $8.6 million contract with the U.S. Air Force in June, its largest government contract to date.

Perhaps the most important factor in the acquisition is the fact that Owens has been able to build a nationwide service organization quickly, spreading from just 13 cities earlier this year to 35 service centers today.

Duke of Energy was little more than a "shell" company with cash, some data processing operations and mineral leases when it went public in the fall. It included Rockie Smith Enterprises, Xedex Corp. and Microlog Corp. Its total assets have risen to $33 million with the purchase of Time Management Software Inc.

A primary business of the firm is the manufacture of microprocessor boards for International Business Machines Corp. personal computers. "Our technology has been written up in nearly every major computer trade journal," said Gary Ammon, the Duke of Energy's chief financial officer.

"We're manufacturing products and we needed a major distribution system," Ammon said. "In addition, we have new products and innovations that we need to bring into the market, and we want instantaneous response."

Terminals Unlimited "has a nationwide computer service structure that we're very interested in utilizing. There has never been a computer service group that has had their basic capacity, specifically in the microcomputer area," he added.

According to Owens, Terminals Unlimited is "by far the dominant force in terminal distribution" in the Washington area, an example of the growth pattern that has spawned not only a large computer industry in the Washington area, but also a series of auxiliary businesses to serve it.