THERE are those who caution potential investors in the new free market China against being dazzled by the potential of ''selling just one shoe to a billion Chinese''. And yet off the salesmen go, taking their know-how and their goodwill and all wide-eyed at the prospect of all that profit. Some would-be China traders have made enormous fortunes, others have been burnt badly. The latest entrepreneurs to make a bid for to sell a billion shoes have been the telecommunications giants such as AT&T and the ''Baby Bells'' of the US, and Alcatel and Ericsson of Europe - and hot on their heels have come the broadcasting moguls. And so executives from the major cable and satellite hardware suppliers such as the Americans Scientific Atlanta, General Instruments Magnavox, Jerrold Communications, Nexus, Echosphere and Ecostar have all been trying to cut deals, not only with the central government but also with state and non-state organisations in almost all the 23 Chinese provinces. According to some estimates China has 140 million television sets and 20 million cable subscribers in place. That's why the world's largest cable TV system operator, Telecommunications Inc, has been banging on Beijing's door and so have the likes of programmers Warner Brothers, ESPN, CNN and the BBC. All have been looking at China for years and some are beginning to feel they are on the verge of a breakthrough. But none, so far, has done so. So, when Mr Rupert Murdoch, the boss of News Corp which has a controlling stake in South China Morning Post (Holdings), owners of Britain's BSkyB satellite network and controller of the US Fox Television network and the 20th Century Fox film studio, makes a trip to three cities in China to check out the possibilities, something must be cooking. It seems Mr Murdoch smells profit and is willing to consider a massive investment in a Chinese economy of 1.2 billion people whose wealth is growing at 13 per cent a year. His involvement in China goes back to 1987 when Fox signed a barter deal with China Central TV to provide the national four-channel network with 26 feature films a year in exchange for the right to sell and share the revenue from advertising. Other deals have followed and Fox provides general programming from its massive library with low-grade soaps such as Dynasty finding big audiences not only on CCTV but also on wealthy Guangdong provincial TV. ''Really anything we do in Asia is done with an eye to China,'' said a Fox executive speaking in Hongkong. ''China is the big one in many ways'', even if the cable market was not yet mature enough to produce a profit for an investor. But even so, ''it is reasonable to look at satellite delivered services. You should realise that the agenda here could be the same as for BSkyB in Europe'', said the executive. Given cable is nowhere near well enough developed in China to produce a fast return and that BSkyB is one of the few true direct-to-home television systems in the world, the play does not seem so far fetched. STAR TV, the six-channel Hongkong-based satellite system, claims a Chinese Government-audited audience of 4.8 million Chinese viewers, with maybe six times that number on a ''guestimated'' basis. Meanwhile, Chinese officials are reported to estimate that 40,000 dishes, priced from 2,000 yuan (HK$2,700), have already been installed by individuals in China, and that within three years 500,000 dishes will be in use. Much to the dismay of the old guard communist cadres, the Chinese Machinery and Electronics Ministry has set a 1993 production target of 30,000 dishes. The satellite business would seem to be unstoppable. However, a Hongkong-based director of Intelligent Communications Ltd, a joint-venture company set up to build and operate cable systems in China, does not see things the same way. He sees cable TV as a real profit centre now. His company, a subsidiary of a Hongkong media group, which wishes to remain anonymous for the time being, signed the joint-venture deal last October with the Wuhan Cable TV Enterprises Ltd. Wuhan is claimed by investors to be on the verge of becoming, in Chinese terms, a centre of technological excellence. ''We are in the process of building a fibre optic and coaxial system with American cable,'' said the Hongkong director, a former senior executive with a Hongkong TV station. Satellite feeds of all kinds are a possibility, agreed the executive, ''but at the moment we aren't interested in that kind of thing. That isn't permitted now and we are doing everything by the book''. Several analysts reckon that when satellite feeds do become officially sanctioned, the programming that will most probably gain the biggest audiences will be in the languages of the country - Mandarin and Cantonese - and will then be followed by much thesame fare as makes big bucks in the rest of the world. ''Chinese-language soaps will do well, but so will Rambo,'' said Mr Kevin John McIntyre, vice-president for network development at STAR TV. ''What does well elsewhere in the world will probably do well in China. ''And never forget that the Chinese educational TV system and its movie industry are currently going through a vibrant period of renewal.'' Even so, Mr McIntyre believes it will take time for commercially viable cable systems to take off in China. Yet there are cable networks of varying kinds developing everywhere across China, not only in the cities but also in tens of thousands of work units of maybe 50 to 200 families. Meanwhile in the major conurbations such as Beijing, Shanghai, Dalian, Changsha, Tianjin, Fuzhou, Guangdong and Chengdu each city hall has, or is expected to permit, a single cable TV network per city within a short time. For all that, delivery of a basic system would seem to be a problem even in Beijing where although there is a two-channel, pay-TV system in operation, the quality of the signals has left plenty to be desired. So much so there are claims the 50,000 households hooked to the 12-hour-a-day system are refusing to pay their monthly fees of six yuan a month, even though the programming would seem to be ideal for a big Chinese city: local soaps in Chinese with dubbedand sub-titled foreign movies on one channel and a mix of CNNI and ESPN aimed at hotels and embassies on the other. However, there are promises of high returns if a system builder and operator can get it right and collect the fees from his subscribers. At present it is claimed the Wuhan network is attracting 20,000 subscribers a month with 100,000 homes ''passed''. By year three of the Wuhan project, the Hongkong partner is forecasting 375,000 households will have signed-up for the system. Connection fees are 180 yuan and subscription is five yuan. The Wuhan system relays seven channels of provincial and national government television plus a mysterious additional ''repackaged'' channel, the contents of which the Hongkong partners refuse to divulge. They will only reveal they are aware viewers demand a great deal more than a diet of state-generated broadcasting. ''Most of the bigger systems often carry propaganda and the house magazines of the state corporations that control them,'' said the Hongkong spokesman. ''We can do a lot better than that.'' Indeed, on the whole, present systems are more like ''mom and pop stores'' than major corporations say those who have been trying to cut deals with Chinese Government officials. ''But forget all that,'' said the Wuhan joint-venture partner. ''The difference between our system and others in China is that we aren't searching for short cuts. We don't use unreliable MMDS [a multi-point microwave delivery system], for instance, and we insist on quality control.'' Apparently Wuhan is different in that the city did not insist the system was put in place within a couple of months. No other city has been so willing to take its time. Even so, China has so often confounded expectations and forecasts that optimism should always be matched by a more sanguine view.