Dire warnings of chaos at ballot boxes, fueled by weeks of legal battles and political skirmishing, largely evaporated yesterday as voting proceeded with relatively few problems and only limited disputes at polling places nationwide.

But lawyers from both parties continued to prepare potential legal strategies as the race remained tight last night in pivotal battleground states such as Ohio.

Election officials and partisan observers reported scattered problems with malfunctioning voting machines, ballot shortages and allegations of dirty tricks in some states. But the main challenge for poll workers throughout the day turned out to be managing the large crowds of voters, who lined up in record numbers in many areas to cast ballots in the hotly contested presidential race.

Voting experts and officials in both parties cautioned last night that serious disputes could still arise. During the contested 2000 race between President Bush and Al Gore, for example, widespread balloting problems in Florida did not emerge as a focus of debate until late into election night.

Party attorneys were also keeping a close eye last night on the record number of provisional ballots cast in many states, which were used for voters whose names did not appear on official rolls and which could not be reviewed or counted until after Election Day. Election officials said the number of such ballots could be high enough to play a decisive role in the closest states, such as Ohio. They said as many as 150,000 provisional ballots may have been cast but that it would take days to count them.

Absentee ballots, which were among the disputed issues in 2000, could also play a role in any fights this year. Florida Secretary of State Glenda E. Hood, noting that absentee ballots may not be completely tallied until tomorrow, said Broward County and Miami-Dade County each received more than 90,000 requests for absentee ballots, and Palm Beach County received more than 70,000.

Hood said there were no indications of any serious problems in the state that produced the butterfly ballots and dimpled chads of 2000.

"We certainly know that all the eyes of the world are upon us," Hood said. "Today, we're seeing the benefits of our election reforms here in Florida."

Indeed, serious complaints were few and major disputes isolated. Doug Chapin, director of Electionline.org, a nonpartisan Web site, said, "The biggest story is what didn't happen. There have been no bigs but lots of littles."

Nonetheless, the legal skirmishing between the campaigns continued yesterday, with the two parties and numerous interest groups heading into court to fight over issues including late poll openings, shortages of voting machines in some precincts and the counting of absentee ballots.

But the biggest problems seemed to be more mundane: late poll openings in some places, long lines everywhere, and broken machinery and a shortage of workers at polling places. The Election Protection coalition, a nonpartisan group of civil rights organizations, reported that in one Florida precinct, the line was the length of three New York City blocks.

After the polls closed, there were also glitches with counting the votes. The Florida Republican Party dispatched a lawyer to Collier County, a heavily Republican jurisdiction, amid reports that the number of votes tabulated by computer didn't match other voting logs, according to GOP spokeswoman Mindy Tucker Fletcher. Fletcher did not know the size of the discrepancy.

The campaign of Sen. John F. Kerry reported after the polls closed that GOP poll watchers stationed in heavily African American precincts challenged only a "handful" out of millions of Floridians' votes. "This was never intended to be voter intimidation," said Wes Maddox, a Republican poll watcher monitoring a low-income, predominantly black district in Tampa's inner city. "We're here to ensure fairness."

Many officials in Florida were also surprised by a lack of widespread problems, other than long lines, at the polls. Kerry spokesman Matt Miller said that "voting is proceeding smoothly" overall, and GOP spokeswoman Fletcher agreed.

"We knew we were okay when Michael Moore couldn't find anything and left the state for Ohio," Fletcher joked of the liberal filmmaker. "I guess we just weren't exciting enough for him."

Streets in Miami were lined with sign-waving partisans, and the early-morning lines were gangly and loud. At an elementary school in a Republican-dominated district in the heart of Cuban Miami, several Democrats complained they were snubbed or treated with hostility by Republican poll managers, but most said a mood of civility prevailed despite long lines that began in the hot sun.

"Everything is smooth and respectful and civil," said Silvia Miniet, 47, after a 60-minute wait at Silver Bluff Elementary. "Everybody has been very helpful, no matter what candidate or what party you are."

GOP challengers were monitoring the polls, armed with packets that included color mug shots of felons the party said were improperly included on the voting rolls. At the urging of the Bush campaign, some of the poll watchers were wearing buttons, hats or T-shirts that said "voting rights counselor."

In Duval County, where four years ago African American voters disproportionately had their ballots nullified because of error-prone punch-card machinery, both parties reported no major voting irregularities. Election Protection coalition volunteers said that by yesterday afternoon, there had been no Republican challenges to voters in black precincts.

At several polling places in Nevada -- particularly the hotly contested minority neighborhoods of Las Vegas -- poll watchers almost outnumbered voters in the middle of the day. At a library in a largely black neighborhood of North Las Vegas, Democratic lawyers from Los Angeles rubbed elbows with NAACP observers who conferred with members of Election Protection wearing "You Have the Right to Vote" T-shirts.

And in New Hampshire, where the parties have bickered for weeks about the eligibility of students from outside the state, several hundred University of New Hampshire students attended a Kerry concert featuring rocker Jon Bon Jovi, then boarded buses to vote at a nearby high school.

People wait in line to vote after the polls closed in Columbus, Ohio, at 7:30 p.m. Walter A. Robinson casts his vote on a paper ballot at Oakwood Baptist Church in New Braunfels, Tex. Only limited disputes occurred at polling places nationwide.A dog and cat go nose to nose as voters line up to cast their ballots in Manhattan Beach, Calif. Heavy turnout was the biggest challenge for election officials in many states.Joann Davidson checks an absentee ballot for the Montgomery County, Ohio, Board of Elections in Dayton.