Washington (CNN) Donald Trump is leading two of his Republican presidential rivals in their home states, topping Sen. Marco Rubio in Florida and Gov. John Kasich in Ohio , new CNN/ORC polls show.

Hillary Clinton, meanwhile, is far ahead of Vermont Sen. Bernie Sanders in both states.

In Ohio, Trump holds 41% to Kasich's 35%, with Texas Sen. Ted Cruz in third at 15% and Rubio in fourth with 7%.

And in Florida, Trump holds 40% to Rubio's 24%, with Cruz at 19% and Kasich at 5%.

The results come less than a week from the March 15 contests in Florida and Ohio, as well as Illinois, North Carolina and Missouri. The primaries in 99-delegate Florida and 66-delegate Ohio are particularly critical for Republicans, since both are winner-take-all.

In both states, large majorities say that if their home-state candidate doesn't win, he should drop out: 71% say Kasich should exit if he loses Ohio, while 66% say Rubio should depart if he loses Florida.

On the Democratic side, Clinton leads Sanders 63% to 33% in Ohio and 61% to 34% in Florida. About 7 in 10 voters in each state say they have definitely decided whom to support.

Ohio's GOP electorate isn't quite as committed to its candidates as are Florida's Republican voters. Overall, 58% have definitely decided whom to support, but Trump does not have an edge on this question: 59% of Trump supporters say they are locked in, and 61% of Kasich's backers say the same.

In Florida, two-thirds of the electorate say they have definitely decided whom to support, including more than 8 in 10 Trump supporters.

The race in the Sunshine State also features sharp divides by education and gender, with Rubio ahead among college graduates and more competitive among women.

And in the general election, Clinton would start with an advantage over Trump in both states, leading in Florida and Ohio by 7 percentage points.

She tops Cruz by 9 in Ohio and runs 2 points ahead of Rubio there. In Florida, though, Rubio tops Clinton by 4, and she's down 1 in a matchup with Cruz.

The polls were conducted March 2-6. The Florida survey includes 1,014 adults, including 264 likely Democratic primary voters and 313 likely Republican primary voters. The Ohio poll includes 1,002 adults, including 294 likely Democratic primary voters and 359 likely Republican voters.

The margin of error in Florida is 5.5 percentage points among Republicans and 6 points with Democrats. In Ohio, it's 5 points among Republicans and 5.5 points with Democrats.