The Supreme Court yesterday vastly expanded the power of states to tax the remote worldwide earnings of large corporations.

The decision means, for example, that the state of Vermont can tax some of Mobil Oil Corp.'s income from a Saudi Arabian subsidiary because Mobil happens to sell gasoline in that state. The amount of the tax, in practice, is determined by the company's total sales in Vermont as a percentage of overall sales.

Until now, most major corporations resisted this form of taxation on the grounds that their business outside the state is unrelated to the earnings within it.

According to corporate legal experts, states may collect hundreds of millions of dollars in additional revenues as a result of the decision. Multinational corporations can be expected to step up efforts already under way in Congress for tax relief.

The justices resolved by a 6-to-1 vote a 65-year legal struggle over the fairness and constitutionality of such taxation, which is currently being fully exploited by only eight states, including Maryland.

All states can already tax the outside earnings of corporations headquartered within their boundaries, though some states, in order to attract business, choose not to do so. New York does not, and so Mobil Oil, which is based there, was paying no state taxes on outside income when Vermont brought the case decided yesterday.

Vermont tried to tax a share of Mobil's dividends from foreign and out-of-state subsidiaries, including Aramco, the giant Mideast firm owned by Saudi Arabia, Mobil and other U.S. oil companies.

In figuring Mobil's tax base, Vermont included its net dividend income from 413 Mobil investments in the U.S. and abroad, including Aramco, Baltimore Gas and Electric Co. and others. The base, from which the tax bill is figured, increased by more than $700 million for the three years in dispute.

Mobil fought Vermont, arguing that the connection between its petroleum sales in that small state and its numerous dividend-paying subsidiaries was too remote to justify the tax.

By winning yesterday, Vermont multiplied by 38 times its tax revenue from Mobil -- from about $2,000 for the three years in question to about $76,000.

"It's horrendous," said Thomas Houser, counsel for the National Association

In the Supreme Court debate, Houser, Mobil and other corporate interests relied heavily on the contention that a company's outside earnings were unrelated to its sales in a particular state.

Justice Harry A. Blackmun, writing for the majority, said the corporations had simply failed to show that. To avoid the tax, he said, a company "must show that the income was earned in the course of activities unrelated to the sale" of products in the state. ". . . All indications . . . are to the contrary, since it appears that these foreign activities are part of [Mobil's] integrated petroleum enterprise."

It does not matter, he said, that the overseas investments belong to some other legal entity, like Aramco. "One must look principally at the underlying activity (in this case, petroleum), not at the form of investment," to determine taxability.

The court also rejected claims that the state taxation illegally imposed "multiple" tax liabilities on corporations.

Yesterday's decision made clear that states can include in a corporation's tax base income from holdings outside the state. It did not say how heavy a tax rate can be imposed. Vermont, and the other states using this method, now figure the rate proportionately to the company's sales within its boundaries.

Blackmun was joined by Chief Justice Warren E. Burger and Justices William J. Brennan Jr., Byron R. White, Lewis F. Powell Jr. and William H. Rehnquist. Justice John Paul Stevens dissented and Justices Potter Stewart and Thurgood Marshall did not participate in the case for undisclosed reasons.