When Mario Vazquez Rana pulled out of United Press International last weekend, a little-known New York company called Infotechnology Inc. emerged as the key player in the latest effort to resuscitate the debt-ridden wire service.

Infotech, a broad-based electronic communications company, was founded in 1980 by Earl Brian, a physician and former secretary of health for California who led the group that has assumed operational control of UPI.

In less than a decade, Brian has transformed Infotech from a small investment company interested in biotechnology and health-related firms to one that operates or controls 20 high-technology companies, mostly in the information technology business. Last September the company changed its name from Biotech Capital Corp. to Infotechnology to reflect its shift in focus.

The company has claimed credit for the turnaround of several companies, including Financial News Network, a cable network that transmits an electronic ticker tape of stock prices and covers daily market activity and other financial and business news. The network is picked up by 27 million homes and businesses.

FNN was losing about $4 million a year when Infotech began investing in the network. In 1986, a drastic reorganization resulted in a profit of $1.2 million on revenue of $15.4 million. By last year, FNN had a profit of $4.6 million on revenue of $36.8 million. Infotech owns about 19 percent of FNN's outstanding common stock.

After investing in FNN, the company moved quickly into information technology. As of June 30, about 71 percent of the value of its investments was in holdings of companies in the information technology industry.

Infotech's assets more than doubled in fiscal 1987, to $101.3 million, compared with $44.6 million in 1986 and with $18.9 million in 1984. The value of its investments also more than doubled in 1987, from $40 million to $85.1 million.

Merrill Lynch & Co. Inc. is Infotech's largest shareholder with a 15 percent stake. Brian holds 13 percent of Infotech shares, 13 percent is held by several institutional investors and the balance is spread among individual shareholders.

With UPI, Brian will have his hands full. The company has been losing at least $12 million a year, and some estimates put the losses at nearly double that amount. The company, which Brian bid for unsuccessfully two years ago, has stymied the attempts of three owners to turn it around.

Yet Ned Patterson, executive vice president for the New York investment banking firm of Allen & Co. Inc., said his firm would be interested in investing in UPI if Brian develops a turnaround plan that Patterson believes will be successful. Patterson said Allen & Co. has invested in almost every deal that Infotech has put together and "not one investment have we been disappointed in. Not one."

Brian, who will develop an overall plan for UPI within four to six weeks, is pinning his hopes on attracting that type of outside investor to fund part of the revitalization of UPI. Infotech has a following of 30 to 40 companies, including Allen & Co., that regularly invests in his deals. Brian believes that if he can come up with a realistic game plan, the companies will be interested in UPI.

"One of the things we hope to bring to UPI is new technology that allows much less expensive delivery" of the news reports, which in turn will allow a much wider distribution to universities and other institutions that cannot now afford the service. Much of UPI is transmitted on telephone lines, which makes the cost prohibitive for many potential customers, he said.

Brian, 45, said the business of providing information technology is expected to grow at a compounded rate of 30 percent in the next five years. "The challenge is improving on those growth rates" by developing better and cheaper technology, he said.

Among the companies in which Infotech owns significant holdings are: The Learning Channel Inc., a privately held cable network that concentrates on adult education, particularly in the areas of business, finance and career growth. The Learning Channel has more than 10 million cable subscribers. Infotech owns about 47 percent of the Learning Channel's outstanding common stock and has four representatives on its 10-member board. Its $3 million investment in the company in 1986 enabled the Learning channel to double its daily programming to 20 hours. Data Broadcasting Corp. is a privately held corporation founded in 1984 to transmit stock quotations and other financial information directly into personal computers. It is available to FNN's 27 million subscribers because it uses FNN's television signal to transmit data, which can then be decoded and stored in personal computers. Brian said he hopes to use this technology to significantly cut UPI's transmission costs. FNN's former president, Paul Steinle, became president of UPI. Infotechnology Publishing Corp., a wholly owned subsidiary of Infotech, publishes High Technology Business, a monthly magazine with a circulation of 200,000. Last year, the group bought The Andrew Seybold Outlook on Professional Computing, a newsletter reporting on the high-technology industry. Infotech is developing a joint marketing and sale program for High Technology Business magazine, FNN and the Learning Channel, saying that the three have similar audiences. Comtex Scientific Corp. markets UPI's electronic database. Infotech owns about 7.9 percent of the shares of Comtex, holdings it acquired from Vazquez Rana two years ago as settlement of a lawsuit that Brian's group filed after losing the bidding battle to buy UPI. Comtex lost $430,793 on revenue of $526,884 in the fourth quarter of fiscal 1987. TI Industries Inc. is involved with electronic mail, telemarketing, software for the securities industry and data processing facilities, and an automated, interactive language translation system. For example, TI provides FNN and Data Broadcasting with the stock quotation information that FNN runs on its cable network and Data Broadcasting transmits to personal computers. In fiscal 1987, TI had profits of $897,950 on revenue of $10.4 million.