If it opens a factory in South Carolina, BMW will join 10 other foreign auto makers that have begun assembling vehicles at "transplants" in the United States and Canada since the early 1980's.

Establishing assembly plants in the United States is attractive because of the considerable size of the North American vehicle market, growing protectionist sentiment and the dollar's weakness, compared with the Japanese and German currencies. Indeed, transplant production has grown into a significant portion of overall North American automotive production, accounting for more than 50,000 jobs in assembly and parts-making operations and about 16 percent of the capacity of 14.8 million vehicles annually, according to Autofacts Inc., a consulting firm in West Chester, Pa.

Among the transplants are the Honda Motor Company's plants in East Liberty, Ohio; Marysville, Ohio, and Alliston, Ontario; the Toyota Motor Corporation's plant in Georgetown, Ky., and others including joint ventures with the Ford Motor Company and the General Motors Corporation.

As North American transplant production has grown, the foreign presence has exerted a vast impact on the auto industry's manufacturing practices, labor relations, Government and trade relations, and on the suppliers that provide parts and materials. The migration has also unleashed fierce competition among states to lure transplant operations with financial incentives.

The United Automobile Workers union, which once represented virtually every assembly worker in the United States and could shut down the entire industry, has failed to organize several transplant factories. The one plant that had U.A.W. representation, Volkswagen A.G.'s ill-fated plant in New Stanton, Pa., began with a strike and lurched from problem to problem before closing in 1988.

Although the U.A.W.'s bargaining power with the Big Three has diminished, BMW may face a fierce union-organizing effort.

Last week, Owen Bieber, the U.A.W. president, told delegates at the union's convention in San Diego that "assuming that BMW follows through on its plans to build a plant in South Carolina, we intend to organize the workers at that plant." Political Incentives

Building plants in the United States has afforded the Japanese auto makers more political influence. As important employers in Ohio, California, Kentucky, Tennessee and elsewhere, Japanese auto makers have won more consideration from legislators in those states. And the American employees of Japanese companies constitute a political force that can write letters to representatives or call them on the telephone. BMW may expect similar help in South Carolina.

State governments have been willing to offer hundreds of millions of dollars in incentives to foreign auto makers to establish plants in their states. The payoff includes thousands of well-paying jobs, the probability that numerous supplier plants will follow and a higher tax base. The automotive trade press reported that South Carolina had offered about $150 million in tax breaks and incentives to persuade BMW, which had also been considering Nebraska.

Except for some Rolls-Royces built in the 1930's, Volkswagens were the first foreign autos assembled in the United States, starting in 1978. But the declining popularity of VW's Rabbit model led to the decision to shut the plant in 1988.

A former VW executive, who spoke on condition of anonymity, said: "The $64 question will be whether BMW can get the level of quality from its workers here that it gets in Germany. I don't think they would have tried unless they think the answer is a resounding yes."