Washington (CNN) Donald Trump and Hillary Clinton each lead their party's respective primary race in Florida, Ohio and Pennsylvania, according to new polls from Quinnipiac University.

But neither Clinton nor Trump fares as well as their top competitors in hypothetical general election match-ups in these three swing states.

Home state politicians don't fare well either -- Ohio Gov. John Kasich, former Pennsylvania Sen. Rick Santorum and Floridians Marco Rubio and Jeb Bush all trail in their respective states.

Facing off against each other, Clinton narrowly tops Trump in Florida, 46% to 42%, while she runs about evenly against the other four potential Republican candidates tested. Clinton and Trump run about evenly in Ohio (43% Clinton to 42% Trump) and Pennsylvania (44% Clinton to 42% Trump).

But the former secretary of state trails retired neurosurgeon Ben Carson in both states, falls behind Rubio in Ohio and trails both former tech CEO Carly Fiorina and Bush in Pennsylvania.

When Trump is matched against either of the other two top Democratic contenders, Vice President Joe Biden and Vermont Sen. Bernie Sanders, the businessman trails by a significant margin in all three states.

But both front-runners still face a long road to their party's nomination.

Florida and Ohio, both currently scheduled to host presidential primaries on March 15, loom larger in the nomination battle than Pennsylvania, where voters will go to the polls in late-April. But if the primary contests on either side remain competitive into the spring, Pennsylvania is one of the biggest prizes slated to vote after March 15.

With support from 28% of Republican registered voters in Florida, Trump tops the GOP field there by 12 points, with Carson in second at 16%. The two candidates who call Florida home follow, with the state's current senator Rubio at 14% and former governor Bush at 12%.

In Ohio, Trump tops Carson 23% to 18%, with Ohio's governor, John Kasich, in third with 13%. Texas Senator Ted Cruz (11%) and Fiorina (10%) follow. Rubio stands at 7% here, Bush at 4%.

In Pennsylvania, Trump has 23% to Carson's 17%, with Rubio behind at 12%. No other candidate hits double-digits, including Pennsylvania's Santorum, who has 2% support there.

Pennsylvania is kinder to the Democratic candidate with ties to the state, Biden. There, Biden holds 25% and stands second to Clinton's 36%, with Sanders at 19%. Clinton holds wider leads in Ohio (40% Clinton to 21% Biden and 19% Sanders) and Florida (43% Clinton to 19% each for Biden and Sanders).

Without Biden in the race, Clinton holds majority support in all three states when his supporters are re-allocated to their second choice candidate, while Sanders' backing hovers around 25%.

Both front-runners, Trump and Clinton, have negative favorability ratings among all registered voters in these three key states, and most in all three say they have doubts about Trump's and Clinton's honesty. Carson and Biden are most apt to be seen as honest in trustworthy in all three states.

Majorities in each state say Trump and Clinton have strong leadership qualities, the only other candidate viewed that way by majorities in all three states is Biden. Biden also leads all others as an empathetic candidate, with more than 6-in-10 in each state saying he cares about the "needs and problems of people like you."

Clinton, Biden and Bush are most apt to be seen as having the right kind of temperament and personality to handle an international crisis as president, about two-thirds in each state say Trump does not have the right temperament for that.

A majority of Ohio voters view Kasich favorably, 52%, but none of the candidates tested are viewed favorably by a majority of voters in all three states. Biden comes closest with 55% seeing him favorably in Florida and 52% in Pennsylvania alongside 47% who view him favorably in Ohio.

Biden's positive ratings in the poll may reflect the fact that he hasn't been campaigning and hasn't recently faced the kinds of scrutiny given to the active candidates in the field. Clinton, notably, saw her favorability ratings plummet after her campaign began in earnest this spring.

Though there is lots of time remaining before voters in these states will head to the polls, a sizable share say they've already started ruling out some candidates. Trump is the top choice in each state as the candidate Republicans say they definitely would not support, with 31% saying they've ruled him out in Pennsylvania and 29% each in Ohio and Florida saying they definitely won't support him.

About 1-in-5 in each state say they wouldn't back Bush, while roughly 1-in-8 in each state say they definitely will not vote for New Jersey Gov. Chris Christie.

Among Democrats, 56% in Florida, 50% in Ohio and 47% in Pennsylvania say they haven't ruled out anyone in the party's field of potential nominees.

The Quinnipiac University polls were conducted by telephone from September 25 through October 5. In Florida, the poll includes interviews with 1,173 registered voters, including 461 Republicans and 411 Democrats. In Ohio, it includes 1,180 registered voters, 433 Republicans and 396 Democrats. And in Pennsylvania, 1,049 registered voters, 427 Republicans and 442 Democrats. The margin of sampling error for results among registered voters is roughly plus or minus 3 percentage points in each state, among Republicans, it is 4.6 points in Florida, 4.7 in Ohio and Pennsylvania, and for Democrats, it is 4.8 points in Florida, 4.9 points in Ohio and 4.7 points in Pennsylvania.