The search for survivors of the collapse of the "floating hotel" oil rig Alexander Kielland in the middle of the North Sea was abandoned tonight, making it almost certain that 123 men perished in the world's worst offshore oil drilling disaster.

"We have no hope of finding any more survivors," reporters were told by Stavanger, Norway, police cheif Carl Wendt. He coordinated the two-day search by British and Norwegian helicopters, planes and ships of 5,000 square miles of sea around the overturned rig just inside the Norwegian sector of the North Sea, midway between Britain and Norway.

Since one of its five huge pontoon legs broke off and the rig capsized in a storm Thursday night, 89 survivors have been rescued and 40 bodies recovered, leaving 83 men missing and now presumed dead. No survivors have been found since nightfall Friday.

Officials of Phillip Petroleum, the American company operating the French-built, Norwegian-owned rig, have finally established that 212 oil workers were on it when the accident occurred. Most were Norwegians, although they were also about 30 British and a few Finnish, Spanish and West German oil workers.

Most of the missing men are believed to have been unable to escape from inside the four-story living quarters on top of the rig's platform, which plunged 100 feet under water when the rig overturned, leaving only the remaining four pontoon feet visible on the surface.

Underwater inspections of the outside of the wreckage by divers and remote-controlled television cameras yesterday and today revealed no signs of life, according to rescue officials. Because many of the living quarters' windows were broken and there were no water-tight compartments inside, Phillips Petroleum official Sto Laerdal said, "We consider the odds are against people still being alive in air pockets."

It was decided not to try to send divers inside the submerged living quarters, according to Laerdal, because of the danger of their lifelines being entangled or severed by debris.

The rig has been safely secured by anchors while Phillips and Norwegian officials decide, with the help of the Dutch salvage experts, what to do next. o"We are studying the feasibility of moving it away some distance," Laerdal said. "Until a final decision can be made on how and when it will be brought back to shore."

Phillips' nearby Edda production platform, for which the Alexander Kielland provided overfolw accommodation, is still not being used although it escaped damage when the hotel rig overturned. But full oil production was resumed today at all other platforms in the vast Ekofisk field, which is operated by Phillips and owned by it and a number of other multi-national oil companies.

The severed pontoon leg of the Alexander Kielland is being towed to Norway. Inspection of the damage to it will begin a Norwegian investigation into the cause of the disaster, which threatens to undermine public and political confidence in the safety provisions for North Sea oil exploration in both Britain and Norway.

This single accident, for example exceeds the death toll of 102 for all the dangerous, deep-water oil exploration in the British sector of the North Sea since the mid-1960s. Previous accidents have been infrequent and small-scale, half involving divers working far underwater and the rest construction and drilling workers on rigs and platforms.

Officials at Phillips, Stavanger Drilling, which owned the rig, and Companie Francais Enterprise Maritime, which built it, said they are baffled about what may have caused its leg to break off and the platform to fall over. Theories ranged from simple metal fatigue not discovered in routine inspections to the snapping in a stormy sea of one of the anchor cables that secured the submerged pontoon legs to the ocean floor.

Unless anchored, so-called semi-submersible rigs like the Alexander Kielland float, being steered with hughe engines, although tugs are required to help them move long distances. Lloyds Register of Shipping reports the existence of 139 such rigs in offshore oil work around the world, some as drilling rigs, some as floating hotels, and some converted from drilling rigs to floating hotels like the Alexander Kielland.

Such rigs were considered almost incapable of capsizing because of the stability provided by their pontoon legs. Most safety precautions against large-scale disaster were designed for blowouts, in which escaping oil or gas could explode and envelop a rig in flames.

Water safety precautions apparently did not anticipate a rig-collapsing so quickly while men were sleeping, eating and recreating rooms, as they were aboard the Alexnader Kielland when it went down. Few of the men rescued or found dead were wearing protective clothing. Some had on only their underwear. Most had to find rafts and lifeboats floating on the water after the rig's collapse had thrown them into the sea.