he last of the witnesses for Microsoft finished testifying on Friday at hearings to determine whether the company should face tougher penalties than those it agreed to in a proposed settlement of the Justice Department's antitrust case. But after eight weeks of hearings, during which nine states seeking tougher remedies presented 15 witnesses and Microsoft called 18, including the company's chairman, Bill Gates, several key questions in the case remain unresolved.

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Judge Colleen Kollar-Kotelly of Federal District Court in Washington, who has little background in either technology or antitrust law, has reserved judgment on the fundamental issue of how broad the scope of a remedy should be.

This week, after a crash course on high-tech industries, which featured the frequent use of arcane acronyms and testimony from executives and experts from all corners of the business, Judge Kollar-Kotelly will finally hear oral arguments on a Microsoft motion to exclude much of the evidence the states presented.

The original judge on the case, Thomas Penfield Jackson of the Federal District Court, ordered that Microsoft be split in two after finding that it had abused its monopoly power in the market for personal computer operating systems by sabotaging the Netscape Navigator browser and Sun Microsystem's Java programming language. Last June, a federal appeals court upheld many of Judge Jackson's findings, but overturned others, and ordered the district court to revise the remedy to fit the new judgment.

Microsoft argues that any remedy must be limited to 12 illegal acts for which the appeals court found it liable. The states say the court should restrain Microsoft from repeating the same tactics in new markets such as network computing, where there are potentially the same threats to its Windows monopoly on PC operating systems once posed by Navigator and Java.

How the judge rules on that question will inevitably shape her decision on whether to adopt any of the states' 20 proposals, or simply approve the proposed settlement agreed to last November by Microsoft, the Justice Department and nine other states.

Judge Kollar-Kotelly will also hear arguments on a motion from Microsoft that she dismiss the case without even considering all of the evidence she heard the last two months because the states have no standing to ask for a remedy that would govern the company's conduct for the entire nation.

The remaining states argue that they have every right to continue the case they began alongside the government and several other states four years ago. The Justice Department has weighed in on their side.

Whatever remedy Judge Kollar-Kotelly prescribes, she also must decide how it will be enforced. That question too will be addressed this week, with Microsoft arguing that appointing a three-person technical committee to oversee the company's compliance is the best approach. The states will urge the judge to appoint a "special master," who they say would be able to act more quickly should problems arise.

What the judge will not hear is last-minute testimony from a witness whom the states hoped to present to support the cornerstone of their remedy proposal, which would require Microsoft to produce a "modular" version of Windows so that computer makers could replace programs like its Web browser with rival software.

Rather than anger the judge and prolong the trial, the states abruptly withdrew the witness, James Bach, last week after Microsoft told the judge it would take several weeks to prepare to cross-examine him.

As the two sides prepare their findings of fact before giving their closing arguments — now scheduled for mid-June — about the only thing they seem to agree on is that Judge Kollar-Kotelly has worked diligently to understand the case.

The nine states pursuing the case are California, Connecticut, Florida, Iowa, Kansas, Massachusetts, Minnesota, Utah and West Virginia. The District of Columbia is also supporting tougher remedies against Microsoft.