NEW YORK, NOV. 6 -- Two and a half years ago, Ernst Aebi sent his daughter Tania, then 18, off on a trip around the world alone in a tiny sailboat because she wouldn't do her homework.

To the astonishment of many she made it, and today New York welcomed home one of its own as frazzle-haired, free-spirited Tania and her world-weary sloop, Varuna, came wallowing in off a windswept sea to a heroine's welcome, including a long and windy missive from President Reagan.

Thousands convened to greet her at South Street Seaport, where she tied up the maroon 26-footer at noon, officially ending the journey of a lifetime.

A fireboat at the foot of Wall Street sent up sheets of spray that made a rainbow in the hard, autumn sunlight and the horns of a dozen support vessels whistled and tooted while people cheered from the docks.

But some things never change.

"Tania, you're in New York now!" shouted Ernst Aebi when he saw his daughter light a cigarette as protectors fended off a mob of wellwishers at the dock.

"Oh, stop nagging me," she shot back, blue eyes blazing. "I'm 21 years old. I don't nag you. They're my lungs."

Turns out one promise Aebi made was to quit smoking when she got home. "But jeez," she said, "I didn't mean the second I got home."

So what did she learn from 30 months at sea, during which she rode safely over the stormy Red Sea, the Indian Ocean, the endless Pacific, the Panama Canal, the Mediterranean and North Atlantic, surviving capsize, a collision with a freighter and long bouts of depression and loneliness?

"I learned that I can do what I set out to do," she said, smiling. "But I'm still not sure I can quit smoking."

The saga of Tania Aebi is one for the books, even if the record books don't seem to want it. She would have been the youngest person to sail around the world alone, eclipsing 21-year-old Robin Lee Graham's record by a matter of days, except for an oversight that rendered her ineligible for the honor.

In Samoa, she gave a hitchhiker a ride 80 miles between islands, and because she never went back to re-run that stretch alone, keepers of sailing records say her 27,000-mile voyage does not classify as single-handed.

Similarly, she can't claim to be the first U.S. woman to sail solo around the world because of the oversight.

Aebi cares not. "It was like taking someone from here to Atlantic City," she said of the side trip in Samoa. "I didn't think it would matter. The island was in sight. To me, a passage was weeks, months."

"The trip was more important than any record," said Olivier Berner, 34, a Swiss single-hander who met Aebi in Vanuatu in the Pacific, sailed alongside her for a good part of the trip, became a close ally at sea and was here to greet her.

Aebi's father hatched the idea to send his daughter around the world alone when she proved a difficult student and refused to go on to college after graduating from an alternative New York high school called City As School.

She was working as a bicycle messenger when he struck the deal: Aebi, a well-known and successful surrealist painter, would buy the $40,000 boat and lend it to her if she would support herself by writing about her voyage as she went. Ten of her articles have since appeared in Cruising World magazine.

Ernst Aebi, a sailing novice, had taken his three children across the Atlantic in a 38-foot boat the year before. So Tania, with only that experience, struck out without even rudimentary navigation skills, learning as she went. "I left knowing nothing," she said with a grin.

Why?

"One day I said yes, we ordered the boat, and then it was too late," said Aebi fatalistically. She finally doped out celestial navigation when she got to the Galapagos Islands. Until then, she went on "pure dumb luck."

Despite the public acclaim, which drew a dozen television crews and a mob of people here today, she doesn't regard her achievement as such a big deal. "I keep wondering why all these people are here," she said. "I try to look at it from the perspective of a nonsailor -- sailing off into the sunset and all that.

"But to me, sailing is just a way of getting from one place to the next. It's nice sometimes and sometimes it's not. Last night I saw a beautiful sunset {off Sandy Hook, N.J.}. I'll remember that a lot longer than three days of vicious storms."

And she'll remember today. New Yorkers, who can turn up their noses at just about anything, are suddenly wild over Tania. Last week, when she briefly fell out of communications during the leg home from Europe, the New York Post ran banner headlines saying she was lost at sea in shark-infested waters.

Several hundred of her fans bought tickets today aboard the 125-foot Andrew Fletcher, which bucked cold, gale-force winds to meet Varuna as she was towed in the last few miles from the Verrazzano Narrows Bridge. (The yacht's small auxiliary engine had died again, as it did often during the trip.)

Many said they had followed Aebi's exploits in Cruising World. Then there was Roy Chou, a fellow bicycle messenger who saw her off in 1985.

She was "the best girl messenger we ever had," he said. "She could do $100 a day, and there's plenty of guys who can't do that."

He said Aebi, who grew up in her father's artist's loft in avant garde Soho, was a hard worker and a sweet, down-to-earth person. "She was so nice, even my girlfriend didn't mind me hanging around with her," he said.

Aebi fielded shouted queries at a crowded news conference on the dock with self-effacing honesty.

"Did you pray?" they asked.

"Oh, all the time."

"Tell us about your worst moments."

"Well, when you see water knee-deep in the cabin, you ask some questions."

"What will you do now?"

"Go through the junk that's accumulated for two years, I guess. See friends."

Regrets?

"It will never be the same as this again," she said later, in a private moment aboard the vessel that carried her as far as a sailor can go. "There's only one first time. It's just a pity it didn't last five years instead of 2 1/2."

Her hands, someone noticed, were shaking. She reached for a cigarette.

A man's voice cut through the din. Her father's.

"Tania!"