All major Democrat and Republican candidates claimed victories on Super Tuesday, but the largest delegate wins went to Hillary Clinton and John McCain.

Map: National Results

McCain now has a commanding lead in the delegate count for the Republican presidential nomination, though his rivals both said they plan to fight all the way to the convention.

Clinton extended her edge over Barack Obama.

With the results still incomplete, McCain won at least 468 Republican delegates Tuesday to 158 for Mitt Romney and 132 for former Arkansas Gov. Mike Huckabee.

Overall, McCain leads with 570 delegates, to 251 for Romney and 175 for Huckabee. It takes 1,191 to win the nomination at the convention in St. Paul, Minnesota.

Clinton Tuesday won 499 Democratic delegates to Obama's 491. Those results are also incomplete, though Obama had more votes in 13 states; Clinton won the popular votes in eight.

Overall, Clinton has 760 delegates to 693 for Obama, with 2,025 delegates required to claim the Democratic nomination in Denver. The Democrats will have several hundred "superdelegates" who do not have to commit before the convention.

Where Wins Came

Clinton captured her adopted home state of New York, along with the biggest state, California. Obama also won his home state of Illinois, but also put together wins in Georgia and Alabama on the strength of black support.

But despite Obama's victories in more than half the Democratic contests, Clinton's victories in California, New York, New Jersey and Massachusetts gave her the advantage as delegates were counted up.

As for McCain, even before he won the Republican primary in California, he was telling supporters he had won "some of the biggest states in the country," including New York and New Jersey. And after running as an underdog for months, he McCain said he doesn't mind one bit his front-runner status.

Romney won in his home state of Massachusetts and in Utah, where fellow Mormons supported him with 90 percent of the vote. And he vowed to "go all the way to the convention."

Huckabee won a series of Bible Belt victories in Alabama, Georgia, Tennessee and his home state of Arkansas and said that he was fine with people calling it a two-man race.

The AP projected how the states will turn out:

Republicans

• McCain: Arizona, California, Connecticut, Delaware, Illinois, Missouri, New Jersey, New York, Oklahoma
• Huckabee: Alabama, Arkansas, Georgia, Tennessee, West Virginia
• Romney: Colorado, Massachusetts, Minnesota, Montana, North Dakota, Utah

Democrats

• Obama: Alabama, Alaska, Colorado, Connecticut, Delaware, Georgia, Idaho, Illinois, Kansas, Minnesota, Missouri, North Dakota, Utah
• Clinton: American Samoa, Arizona, Arkansas, California, Massachusetts, New Jersey, New York, Oklahoma, Tennessee

Romney, sounding defiant, told supporters in Boston, "One thing is clear, this campaign is going on. We are going to go all the way to the convention."

Meanwhile, Democratic rivals Clinton and Obama swapped victories in a grueling national struggle for delegates.

In Chicago, declaring that "it is good to be back home," Obama said that "we don't need the results to know that our time has come," he said. "Our movement is real and change is coming to America."

Heavy Turnout

Election officials across the country on Super Tuesday reported turnout, if not records.

In Massachusetts, more than 1.6 million votes were cast. That surpassed a primary election record in 1980 when more than 1.3 million people voted on a ballot that included Sen. Ted Kennedy and Jimmy Carter on the Democratic side and Republicans Ronald Reagan and George Bush.

In Alaska, police threatened to tow cars at a crowded caucus site in Anchorage.

In Alabama, more than 58,000 new voters signed up in the three months leading up to Super Tuesday.

In Connecticut, strong turnout forced several towns had to photocopy ballots.