When Iraq overran Kuwait early last month, officials of Kuwait's giant state-owned oil company grabbed for their Christmas card lists.

The executives were in London, but the oil company's client records and contract files were at headquarters in Kuwait. A $12 billion-a-year enterprise and one of the world's biggest oil companies, it suddenly had no access to files showing who its customers were or what it was supposed to deliver to them.

"So they took out their Christmas card lists and telexed all those people," company spokesman Ole Bjerregaard said, "and asked them to report on their relations with the company. It worked quite well."

Kuwait Petroleum Corp., unlike the country that owns it, was back in business.

And KPC remains in business, buying crude oil, refining gasoline and selling it at its thousands of Q8 service stations in Europe and Asia, operating a tanker fleet and a California-based drilling subsidiary, and exploring for oil in many countries. The company is much smaller than before because it is no longer selling crude oil from Kuwait's rich fields, but much of the rest is intact.

Wall Street analysts confirmed company statements that the U.S. and British governments have softened their freeze of Kuwaiti assets to allow the oil company to carry out its international transactions. Banks have recognized KPC's management as the legitimate operator of the company, just as other nations have recognized Kuwait's government in exile as the legitimate authority of the state. They are honoring its checks and financing its transactions, according to analysts in New York and London.

Salomon Brothers Inc. analyst Bernard J. Picchi said that KPC controls more than enough assets to make it creditworthy and that there is no reason not to do business with the company. He and other experts said the ultimate issue of the company's ownership is irrelevant to its current day-to-day operations.

"Who owns the company? Is it Kuwait's government in exile? The government of Iraq? Is it the ruling family? Is it the incumbent management? It doesn't make any difference. Let the courts sort it out later," a New York oil expert said. "Right now, it's like any company that's being run in a trust, just carrying on normal business."

According to a KPC statement, the company and its subsidiaries "are the property of the state of Kuwait, whose legitimate government is now outside the country but is in regular contact with these companies."

Rashid Salem Umairi, KPC's chairman and oil minister, was trapped in Kuwait at the time of the invasion, but Nader Sultan, president of its major operating subsidiary, and eight of the 10 directors either were outside Kuwait or escaped later. They are now based in London, reshaping KPC to its new profile as an international company known in industry parlance as "crude short" -- that is, lacking enough crude oil to supply its refineries and forced to shop for it on the world market.

The existence of Kuwait Petroleum Corp. is a reflection of the changes that have swept the world oil market in the past 15 years.

Before the mid-1970s, most of the large oil-producing countries sold or leased production rights to privately owned international oil companies. So-called "downstream" operations -- refining and marketing -- were carried out by the major oil companies in the consuming countries.

In Kuwait, the oil rights were held by British Petroleum Co. and Gulf Oil Corp. But Kuwait, taking its cue from Iraq, nationalized the joint venture in 1975, leaving Gulf and BP "crude short" just as KPC is now.

Kuwait was a pioneer among oil-producing countries in developing a state-owned company and turning it into an international enterprise engaged in all aspects of the petroleum industry.

According to calculations by the trade journal Petroleum Intelligence Weekly, KPC is -- or was -- the world's 10th-largest oil company, right behind Texaco Inc. The biggest is Saudi Aramco, the Saudi equivalent of KPC. Royal Dutch/Shell Group is second, Exxon Corp. third.

KPC does not reveal details of its finances, but it reportedly had $12.3 billion in revenue in 1988 and a profit of $433 million.

According to Petroleum Intelligence Weekly, those figures made KPC one of the least efficient of the major oil companies when measured by net income per barrel of sales: $1.31. For the most efficient, Atlantic Richfield Corp., the figure was $5.76.

Analysts with inside knowledge of KPC said the low profit reflects a casual management style that allows individual Kuwaitis to run wholly owned but semiautonomous subsidiaries more or less as they please.

According to these analysts, some KPC units operate as a loss: Kuwait Foreign Petroleum Exploration Co., which is exploring for oil in 14 countries, and possibly Kuwait Oil Tanker Co., with a fleet of 30 oil and gasoline tankers.

As a country, Kuwait derived most of its income from financial investments in the United States and Europe, not from oil. According to a former KPC employee now living in Washington, "It never mattered if they ran KPC as an efficient business and made money."

But now it will matter, he said, because KPC and its most important surviving unit, Kuwait Petroleum International, will have to compete in the tight world market for supplies of crude oil for its three refineries in Europe. Initially at least, the company has been lucky, said spokesman Bjerregaard.

"We had significant stocks of crude and refined products at the time of the invasion," he said.

In addition, Bjerregaard said, KPC had 15 million barrels of oil afloat, about a 40-day supply. That oil was shipped out of Kuwait before the invasion and is essentially free to the company, Bjerregaard said, because there is no way to send payment back to Kuwait.

Having those supplies available, he said, gave the company time to negotiate for new supplies of crude for its refineries.

KPC has arranged for oil from Saudi Arabia, Norway and the United Arab Emirates to keep its European refineries and gasoline stations supplied, he said.