As expected, Republican presidential frontrunner Donald Trump stood out in the first round of the party's debate for the 2016 GOP presidential nomination in Cleveland on Thursday.

The candidates jabbed each other, issued quotable remarks and heaped criticism on the Obama administration and Democratic frontrunner Hillary Clinton. However, there was no clear winner or loser, leaving the 17-candidate GOP field intact.

Trump arrived to an explosive start as he drew audible boos from the audience at Quicken Loans Arena as the Fox News debate moderators asked him provocative questions. Moderator Bret Baier first asked all 10 candidates onstage whether they would pledge to back the eventual nominee. All the candidates said yes—except Trump.

"I cannot say 'I have to respect the person, who is not me'.... I can totally make that pledge if I'm the nominee: 'I will not run as an independent'. We want to win, and we will win," Trump said.

"But I want to win as the Republican. I want to run as the Republican nominee," he added.

Citing political experts, Fox News anchor Bret Baier said Trump's willingness to run an independent campaign against the eventual Republican nominee "will almost certainly" give the US presidential election to the Democrats.

"I mean, this is what's wrong. He buys and sells politicians of all stripes. He's already hedging his bet on the Clintons, okay?" presidential rival and Kentucky Sen. Rand Paul cut in.

Trump got into more trouble when moderator Megyn Kelly brought up his past comments on women. "You've called women you don't like, 'fat pigs,' 'dogs,' slobs, and disgusting animals," Kelly said.

"Only Rosie O'Donnell," Trump quipped.

"No it wasn't. For the record, it was well beyond Rosie O'Donnell," Kelly said. "Your Twitter account has several disparaging comments about women's looks. You once told a contestant on 'Celebrity Apprentice' it would be a pretty picture to see her on her knees. Does that sound to you like the temperament of a man we should elect as president?"

The question appeared to jolt Trump who responded by saying that the problem with America is the trend toward being "politically correct." He told Kelly that if she didn't like what he said about women, "I'm sorry."

"I think the big problem this country has is being politically correct," he said. "I've been challenged by so many people and I don't frankly have time for total political correctness. And to be honest to you, this country doesn't have time either."

Trump then tried to shift the discussion to the bigger issues. "This country is in big trouble. We don't win anymore. We lose to China. We lose to Mexico, both in trade and at the border. We lose to everybody. And frankly, what I say — and oftentimes it's fun, it's kidding, we have a good time — what I say is what I say. And honestly, Megyn, if you don't like it, I'm sorry. I've been very nice to you, although I could probably maybe not be based on the way you have treated me. But I wouldn't do that," he said.

In the same debate, Trump admitted that he gave money to politicians so that he could later get favours from them. He cited Democratic presidential frontrunner Hillary Clinton who, he said, benefitted from the donation he made to the Clinton Foundation. In return, Trump said he asked the Clinton couple to attend his wedding in 2005, and they did.

"I will tell you that our system is broken... Before two months ago, I was a businessman. When they call, I give. And you know what? When I need something from them, two years later, three years later, I call them. They are there for me. And that's a broken system," Trump admitted.

"I'll tell you what: with Hillary Clinton, I said 'Be at my wedding' and she came to my wedding. You know why? She had no choice. Because I gave," Trump said.

In his piece for Vox Policy and Politics, writer Ezra Klein branded Trump a man without shame as he sees no problem in admitting that he tried to buy politicians to benefit himself and his company.

Charles Krauthammer, political analyst and contributor for Fox News, said Trump was out of place in the debate that saw him jousting with Kelly, who challenged him on his previous comments about women.

"When you think about it, when he is free-form, when he is uninterrupted and when he can do the flight of ideas, when he can go on his own and ramble – he's entertaining, he's sharp and he's actually amusing," Krauthammer said.

"But here when he was controlled and in a tight setting, he was lost for much of the debate," he added.

Late Friday afternoon, Trump fired back, blasting Krauthammer with a series of tweets:

"The hatred that clown @krauthammer has for me is unbelievable—causes him to lie when many others say Trump easily won debate."

"...Dopey@krauthammer should be fired. @FoxNews"

"@FoxNews you should be ashamed of yourself. I got you the highest debate ratings in your history & you say nothing but bad..."

Trump claimed he was mistreated by the Fox News team. He also launched Twitter attacks on Kelly and pollster Frank Luntz, who conducted an on-air focus group that gave Trump an unfavourable review after the debate.

Michael Cohen, special counsel to Trump, said Fox News' coverage of the debate was clearly part of a "coordinated" effort to stop Trump's "movement."

After the debate, Fox News featured Luntz's focus group together with the commentary from hosts and guests who described Trump's performance as a "collapse."

Cohen said this as an "insidious" attempt to spread the perception that Trump lost the debate.

The question on the morning after the debate was: Who won?

Political pundit seemed to agree that there was no clear winner, except perhaps former HP exec Carly Fiorina who dominated the early, 5 p.m. preliminary debate among those outside the top 10 Republican circle. Fiorina's performance shook social media, and following the featured main event, the debate among the top 10 candidates, she even out-trended Trump on Twitter.

Fiorina stood to gain the most from the debate, considering her low ratings in the polls. "I think a lot more people know who I am and know that I'm running for president," she told Fox News.

In the main debate, Ohio Governor John Kasich branded himself as the compassionate conservative. Senator Marco Rubio focused on policy and his criticism of the Obama administration. New Jersey Gov. Chris Christie almost out-Trumped Trump with his brash remarks. Former Florida Governor Jeb Bush found himself on the defensive and was seen evidently trying to avoid mixing it up with Trump.

In perhaps the most explosive moment of the debate, New Jersey Governor Chris Christie and Kentucky Sen. Rand Paul clashed with Christie reprising his criticism of the senator for opposing the bulk collection of Americans' phone data by the National Security Agency.

Paul replied that he's "proud of standing for the Bill of Rights," but Christie struck back, calling his stance "completely ridiculous."

Other candidates also gave a good account of themselves. Retired neurosurgeon Ben Carson called Hillary Clinton the "epitome" of the progressive movement.

Rubio sparked laughter in the audience when, upon being asked about his faith in God, he said: "I think God has blessed us, he's blessed the Republican Party with some very good candidates. The Democrats can't even find one."

Rubio also vowed to repeal and replace ObamaCare if he is elected president.

Former Arkansas Gov. Mike Huckabee denounced Planned Parenthood, accusing abortion providers of "selling" foetal parts "like they're parts to a Buick."

Senator Ted Cruz also blasted Planned Parenthood and vowed to cancel the Iran nuclear deal and Obama's executive orders if he wins the election.