Skylab, the biggest thing man has ever sent to space, returned to Earth today in an apparently harmless shower of debris over the Indian Ocean and Australia.

While its return had spawned much humor and some real fear, most of the 6-year-old, 77-ton orbiting laboratory simply fell into the sea. Some of the heavier fragments apparently came down in southwest Australia, but by late today space agency officials had received no word of injury of damage.

There were uncomfirmed reports that some debris had been found.

President Carter sent a message of concern to Australian Prime Minister J. Malcolm Fraser, saying that he had instructed the State Department to "offer any assistance you may need."

Skylab's end came on its 34,981st orbit, a path which, to the unconcealed joy of NASA officials, took it over vast stretches of ocean and minimal numbers of people.

But the giant satellite did not die without a fight. It remained intact in the atmosphere far longer than had it predicted before breaking up into what a man in Perth described as a "quite spectacular" spray of hundred or so glowing pieces.

An airline pilot flying at 28,000 feet told National Aeronautics and Space Administration officials here that Skylab turned "a distinct blue glow, then orangy red, you could see the breakup of it start to occur."

The pilot said he believed that as the "very bright orange ball . . . giving off sparks with a long trail" broke up, it was over the land.

"The surprise is over," said Skylab flight director Charles Harlan at a news conference in tne Manned Space Flight Center. "Skylab is on the Earth somewhere."

Exactly where was not immediately clear.

As the day wore on after Skylab's entry into the atmosphere about 12:32 p.m. (EDT), officials continued to try to reconstruct the exact breakup area.

The North American Air Defense Command (NORAD), which tracks falling space objects, initially estimated the splashdown of Skylab's heaviest parts at 42.87 degrees south, 105.97 degrees east, about 700 miles off the southwest coast of Australia.

Tonight, however, based on the pilot's report, NORAD fixed the impact area of Skylab's heaviest remnants as 31.8 degrees south, 124.4 degrees east, near the town of Kalgoorlie. The time was estimated at 2:37 EDT.

Lighter remnants trailed behind in the Indian Ocean, probably covering less ocean than the 4,000-mile stretch officials had predicted.

Harlan and space officials in Washington expressed satisfaction with that wreckage path, the apparent result, in part, of a NASA decision in the early hours of today to begin tumbling Skylab through its final orbits much sooner than had been planned yesterday.

That action prolonged Skylab's life by 18 minutes, putting it well into the south Atlantic before it began to break up.

The decision to prolong the orbit came after a succession of estimates Tuesday, increasing the likelihood that Skylab's impact point would be in populous areas of the east coast of North America, Maine, Nova Scotia, Montreal and the Canadian interior all became exposed as an ever-earlier reentry was forecast.

Both Harlan and NASA Deputy Associate Administrator Richard G. Smith said they would make the same decision, for an early tumble, again, given the information available shortly after midnight today.

So a little before 1 this morning, Mike Hawes, a 23-year-old computer control officer, gave five four-digit numbers - 1062, 1426, 1313, 1427 and 0888 - by telephone to controllers in Santiago, Chile. At 2:23 a.m. (EDT) Skylab received those coded signals, telling it what maneuvers to perform to begin its rolling tumble for its last six orbits in space.

It was then about 92 miles above the Earth.

Within five hours, Skylab crews working the overnight shift here were on the rooftop, scanning the sky for the brilliant moving glow of Skylab, which they caught over the Gulf of Mexico in its last pass visible in the Houston area.

"I was just sorry it had to end," said NASA worker Cindy Majors, 27, who, three hours before watching Skylab's pass, had tooted a New Year's Eve horn indicating that she had successfully commanded the craft's gyroscopes to shut down.

Shortly after 9 a.m. (EDT), NASA cut in half the five-hour period projected for Skylab's reentry into the atmosphere. Instead of a time frame of 8:48 a.m. to 1:48 p.m., officials projected its return as sometime between 10:41 a.m. and 1:01 p.m.

Skylab began its final orbit about 80 miles above the Equator over the Pacific Ocean, moving northeast toward Portland, Ore., and gradually losing altitude all the way. It passed safely over the Pacific Northwest, Canada and the population centers NASA wanted to avoid.

As it moved southeast over the Atlantic, slipping steadily lower, flight controllers in Bermuda reported that even Skylab's flimsy, windmill-like solar panels were still intact, and they stayed that way as the craft moved along the southwest coast of Africa.

Most of it held together even as it legt the range of trackers on Ascension Island, with transmissions from the plunging craft breaking up as it moved farther away. The only sure sign of Skylab's dissapearance was its failure to appear on subsequent tracking screens in the Pacific.

At 12:31 p.m. (EDT) Skylab control announced that NORAD had confirmed that "some portions of Skylab have completed reentry." Then came a NORAD preliminary report that "Skylab has, in fact, impacted."

Just where, no one knew for hours.

But almost immediately there were reports of sightings from Australia, including that of the airline pilot who said he was flying 130 miles northeast of Perth when he saw the glowing disintegration of Skylab an estimated 300 to 400 miles away and moving from southwest to the northwest.

The pilot, identified only as a Bill Anderson, said it appeared that Skylab broke over land along the southern coast of southwest Australia. In a telephone interview with Anderson, Harlan said it was consistent with U.S. projections, and later added that the pilot's account was not only graphic but highly credible.

Harlan at an afternoon news conference spoke for many, however, when he said of the fallen debris, "I don't know where it is now."

The end of Skylab was market by controllers who shared a blue and white frosted cake in the shape of Skylab. As in real life, the solar panels were the first to go, six years and two months after the craft's troubled launching and 16 months after the reactivation of the abandoned craft in an effort to try to control its unavoidable reentry.

It had been used by three space crews for a total of 171 days in space, and the craft cost $293 million in a program of space exploration that cost $2.5 billion.

The ground crews here at the space center who nursed Skylab to its death were on loan from the space shuttle program, working in crowded makeshift quarters.

The control room where Skylab's launch and journey into space had been monitored on May 14, 1973, served today only as a television studio for the three national TV networks.

"I got to thinking you couldn't kill this spacecraft," said Harlan about his watching it last longer than anyone had imagined. He spoke highly of the craft, its continual recoveries from trouble throughout its time and travels in space. He derided those who have lumped the falling star of Skylab with flawed airplanes, cars and nuclear power plants.

"I would be the first to stand up for American technology," he said.

So, finally, Skylab is back, even if no one knows quite where, and it would appear that throughout its life in space officials knew better where it was high above the Earth than they could determine when Skylab finally came home. CAPTION: Picture, Pieces of Skylab dot the sky south of Perth, Australia, during the breakup of the space vehicle yesterday over the Pacific Ocean. AP