Donald Trump stole the show during the first Republican presidential debate in Ohio - with rapturous applause and booing from the audience along the way.

The outspoken billionaire refused to pledge he would throw his support behind the person who secures the Republican Party's nomination.

He also suggested that he may run as an independent if he is not chosen - which could split the vote and help the Democrats regain office.

However, Mr Trump said: "I want to win as a Republican, I want to run as a Republican nominee."

During the Fox News debate, Mr Trump also faced difficult questions about the demeaning comments he has made about women on social media.

In response, the longshot candidate said America shouldn't have time for political correctness.

And he warned the country could be losing ground to China because it wasn't focusing on the economy.

He also defended his remarks that Mexican "rapists" and criminals were crossing illegally into the US.

He insisted that he had received those facts from border patrol officials.

"We need to build a wall and it has to be built quickly," he said.

Mr Trump also faced scrutiny over his business practices - especially the fact that four of his ventures had gone bankrupt.

The other nine candidates on the stage also received a grilling from moderators Megyn Kelly, Chris Wallace and Bret Baier.

Bush: Iraq war was a mistake

Jeb Bush responded to concerns that he would follow his father and brother into the White House - insisting that he had established his own record in office.

He also admitted that the Iraq War initiated by his brother, George W Bush, when he was president was a mistake.

The Governor of New Jersey, Chris Christie, was grilled on the economy - the main concern for voters in his state.

He insisted that in the years since he took office, things had improved considerably.

Rand Paul vowed to stop ISIS by "not funding them and not arming them".

The candidates were also asked how they would defeat the extremist group in 90 days.

Texas Senator Ted Cruz said: "If you wage jihad on America, you are signing a death warrant. We need an American president that shows courage."

Neurosurgeon Ben Carson ducked a question about whether he would bring back waterboarding if elected US president.

A Facebook user asked the candidates about the size of government - and whether or not they would shrink the expenditure or powers of bodies such as the IRS or the Department of Education if elected.

"This is power that should be shifted back to the states," Mike Huckabee said.

The debate came hours after the remaining seven hopefuls took place in a pre-debate forum outside of primetime.

The forum was dismissively called the "kids' stage" by some analysts.

Two participants in that forum, the former Texas Governor Rick Perry and businesswoman Carly Florina, were quick to criticise Trump.

Ms Florina asked: "What are the principles by which he would govern?".