ASHINGTON, Oct. 7 — The phrase "Virginia versus Maryland" may bring to mind a college football game, but at the Supreme Court, at least, it identifies a centuries-old grudge match over rights to the Potomac River, which forms most of the boundary between the two states.

The actual ownership of the Potomac is undisputed: it belongs to Maryland, under a grant from King Charles I to Lord Baltimore in 1632. And as far as Maryland is concerned, that is basically the beginning and end of the story.

"First in time, first in line," Andrew H. Baida, a Baltimore lawyer arguing for Maryland, told the justices on Tuesday. "Maryland's title has not changed one iota in nearly 400 years."

In the particular chapter of the dispute now before the court, Maryland's position is that its legal "dominion" over the river gave it regulatory authority and required Virginia to get Maryland's permission before building a 725-foot-long pipe to extract drinking water from near the midpoint of the river's channel in the western part of the Fairfax County, Va. The project's purpose is to serve the needs of Fairfax County, a rapidly growing Washington suburb that competes for business with Montgomery County, Md.

Virginia argues that the 1632 charter is only one point in a web of contradictory events that taken as a whole defeat Maryland's claim to sovereignty. These include a 1785 compact that gave the citizens of each state the "privilege of making and carrying out wharfs and other improvements" from their respective sides of the river.

The compact was "plain and unambiguous" in giving Virginia the right to decide for itself how to meet its water needs, Virginia's lawyer, Stuart A. Raphael, told the court. "Ownership is not dispositive in a dispute between states over supplying water to citizens of both states," Mr. Raphael said.

The pipe was built two years ago, with Maryland yielding after it lost a series of rulings in its own courts stemming from its refusal in 1996 to issue a permit to the Fairfax County Water Authority. But neither state regards the dispute as moot.

"This case is important," Mr. Raphael told the justices, because "if Maryland prevails, they can control growth and development in Virginia."

Virginia had opened a separate track in the dispute early in 2000 by filing a case against Maryland directly in the Supreme Court under the court's "original jurisdiction" to resolve cases between states. As they usually do, the justices appointed a special master to take evidence and make recommendations. The master, Ralph I. Lancaster Jr., a lawyer from Portland, Me., tried to get the two sides to settle their dispute. When that failed, Mr. Lancaster issued a report that endorsed Virginia's position. Maryland's challenge to Mr. Lancaster's report led to Tuesday's argument in Virginia v. Maryland, No. 129 Original.

Based on the reaction of the justices, Mr. Baida, a former solicitor general of Maryland, faces a battle in persuading the court to reject the special master's recommendation.

"How is Maryland adversely affected by this pipe?" Justice Ruth Bader Ginsburg asked, adding, "Is your argument just that `we're sovereign' or that `our own people won't have enough water' "?

Mr. Baida conceded that the Maryland courts had found there would be no injury to the state. But Maryland had wanted to prod Fairfax County into coming up with a "less intrusive alternative," he said.

Justice Antonin Scalia said that if Maryland's objection boiled down to "it's ugly," Maryland should have thought of that in 1785 and included a clause in the compact giving itself the right to veto ugly projects.

Tuesday's arguments were the first of the court's new term, and the justices approached their task energetically. The morning's first argument, involving a Texas case, was particularly lively despite the technical nature of the question: can a state that enters into a consent decree by which it agrees to comply with a federal law then invoke sovereign immunity in claiming that a federal court cannot order it to adhere to the decree's terms?

The case, Frew v. Hawkins, No. 02-628, began in 1993 as a class-action lawsuit on behalf of Medicaid recipients who accused Texas of failing to provide required services for children. The litigation ended in 1996 when Texas agreed in a federal consent decree to make improvements in its Medicaid program.

Two years later, the plaintiffs went back to court to argue that Texas was not living up to its agreement. The court held that while the state itself was immune from the enforcement suit, the officials themselves could be sued and be held to the terms they had agreed to. But the United States Court of Appeals for the Fifth Circuit, in New Orleans, disagreed and found that the officials could not be required to take any steps that went beyond the precise boundaries of the federal law.

The Bush administration joined the plaintiffs in challenging that ruling, and there appeared to be a clear majority in the argument on Tuesday for overturning it. If state officials could not be bound by a consent decree, why would the other side ever agree to settle a case, Justice Scalia asked R. Edward Cruz, the Texas solicitor general. "That's crazy," Justice Scalia added. "You're telling them that they accomplished nothing and that they have to re-initiate the whole thing."

The plaintiffs' lawyer, Susan F. Zinn, offered two grounds on which the appeals court could be overturned: that the state officials waived their immunity when they accepted the decree and submitted to the district's court's jurisdiction in the first place, and that a suit against state officials to remedy a continuing violation of federal law is a well-established exception to the Supreme Court's immunity doctrines.