Mr Turner is regarded as one of the founders of US cable television. In 1985, he made his first attempt to take over one of the big three TV networks, CBS. He was beaten to it by Larry Tisch, who became CBS chairman. The same year he set up CNN. Few people outside the US had heard of it before the Gulf War. After it, everyone had.
TBS has a fistful of other businesses besides CNN. They include four more cable channels, MGM's film library, sports programming, and two film production companies, New Line Cinema and Castle Rock Entertainment. All these acquisitions left TBS short of capital, forcing it to sell shares to two other media giants, Time Warner and the cable network operator TCI.
But it is these shareholdings that have caused Mr Turner so many troubles. Time Warner holds 18 per cent of TBS and TCI 21 per cent, and he can do little without their agreement. It is difficult to accommodate the various ambitions of three media moguls, and this trio have at times resembled three cats in a sack.
Remarkable reversals of strategy have been attempted over the past year. Last summer, Mr Turner was dancing around CBS for the second time, but by the autumn he had turned his attentions to another TV network, NBC.
The problems were Time Warner and TCI. US media ownership rules do not allow one company to own a cable network and a national TV network in the same market, and Time Warner has a cable network in New York. At one stage, Time Warner was thought to be trying to swap its TBS stake for one of the TBS companies, while negotiations to sell its stake to TCI came to nothing. By spring 1995, talks between TBS and NBC had collapsed.
But things really hotted up this summer, with the third US network, ABC/Capital Cities, being snapped up by Disney, and Westinghouse making a $5.4bn agreed bid for CBS.
Time Warner's proposed take- over of TBS in a share swap deal would seem to bring Mr Turner's ambition to own a TV network to an end. It is not a straightforward deal, since TCI and Time Warner's minority shareholder Seagram must both agree. What will become of a proposed $2bn deal between TBS and Bill Gates' Microsoft, and an incomplete deal by Mr Turner to purchase Samuel Goldwyn Mayer, is not yet clear. Last summer, Mr Turner predicted all three US TV networks would have changed hands within the next three years. He made no predictions about his company.