Tele-Communications Inc., the Denver-based cable television company that has proposed investing $30 million to bail out District Cablevision Inc., is the largest operator of cable systems in the nation and has a reputation for aggressively acquiring shares of smaller companies.

With more than 3.6 million subscribers nationwide, the firm owns, operates or has an interest in more than 700 cable systems.

The company, which had $1.6 billion in assets and $449 million in revenues in 1984, has shown a preference for buying existing systems or purchasing an interest in such systems, rather than seeking an initial franchise, said Carolyn Baker-Smith, assistant to the company's chairman.

"TCI takes a minority interest in cable operations and they borrow heavily," said Theodore Filitis, vice president of Alliance Capital Management Corp., a New York firm that invests heavily in the cable industry. Filitis characterized TCI's history of acquisition as as "the most aggressive by far" in the cable field.

The company prefers to steer clear of the politically charged franchise award process, which in the District and elsewhere has led to over-promising and backtracking by firms that cannot meet their contractual agreements. Notable exceptions to the rule are three Chicago cable franchises the company obtained.

Mayor Marion Barry has expressed concern that TCI's offer to invest $30 million could result in a loss of local control over the cable system. Some financial analysts say, however, that TCI does not have a history of taking over faltering companies, with the exception of the Pittsburgh cable system.

In addition to its partnerships with smaller corporations, TCI operates cable systems in joint ventures with E.W. Scripps Co., Taft Communications and Knight-Ridder.