An attempt to end the long-simmering battle over the right of Walter Polovchak to remain in this country disintegrated today in complex arguments before a federal appeals court panel here.

Polovchak, 17, refused at age 12 to return to the Soviet Union with his parents, who had lived here for six months.

Attorneys for the Justice Department and the American Civil Liberties Union seemed poised today to agree on an ACLU motion that would have sought the dismissal of a key order from a lower court judge, allowing for Polovchak's parents to return to the United States to urge their son to join them in the Ukraine.

But under questioning by the judges, each side began voicing reservations about the other's intentions and the possibility that the youth could be exposed to coercion from the Soviet Union to return with his parents.

After more than an hour of verbal jousting, the hearing adjourned with the judges having made no decision on the lower court's ruling, and the ACLU having withdrawn its motion.

The issue is likely to be made moot soon. On Oct. 3, Polovchak will turn 18 -- of legal age under U.S. and Soviet law, so his parents would no longer be able to claim legal control over him.

Polovchak's lawyer, Julian Kulas, assured the youth after the hearing that he could "go back to school and resume your studies."

Polovchak has lived in America since 1980, when his family emigrated here from the Soviet Union.

But when his parents decided to return to the Ukraine later that year, the youth fled the household rather than accompany them.

A legal fight ensued over the parents' rights to seek to have their son join them in their homeland.

His fate has been the subject of national debate ever since.

Today, Polovchak said, he believes "the whole case is over. I feel better now."