WASHINGTON – Donald Trump’s much-discussed fingers have tightened their grip on the Republican presidential nomination, strengthened by a dominant performance Tuesday as the primaries entered their second half.

Key primary wins brought Trump closer to the magic 50-per-cent pace he’d need to secure a first-ballot victory and avoid a challenge at the Republican party’s summer convention.

He entered the evening with about 40 per cent of the delegates pledged so far, and appeared likely to end it hovering somewhere around the 45-per-cent mark which still leaves him short of that coveted clip.

Trump was poised to win as many as four of the five states voting. He easily won the greatest prize, Florida; held a solid lead in early results in Illinois; and held smaller advantages in North Carolina and Missouri.

“Nobody in the history of politics has received the kind of negative advertising that I have. Record, record, record. Mostly false — I wouldn’t say 100 per cent, but about 90 per cent,” Trump told a jubilant rally in Florida.

“You explain it to me — because I can’t. My numbers went up.”

His biggest triumph was knocking out the great-right-hope of party brass Marco Rubio — Trump beat the young senator in his home state of Florida, forcing him to withdraw from the race.

It was sweet revenge: Rubio had worked an old gag into his stump speech about the size of Trump’s fingers, and used it to make unflattering insinuations about other parts of his anatomy.

Trump got the last laugh. He obliterated him by nearly 20 percentage points on his own turf — prompting Rubio’s immediate resignation, to the delight of Democrats who’d feared the youthful lawmaker.

Trump picked up big blocs of delegates, who will actually pick the Republican nominee at the July convention. As the nomination race officially passed its halfway point Tuesday, it held its first winner-take-all contests Tuesday.

Until now winners in each state had to split delegates proportionally. But delegates are now being awarded in bulk to the No. 1 finisher in some states, with Trump winning most.

Trump appeared likely to end the evening with about 650 delegates; Texas Sen. Ted Cruz with about 400; Rubio with less than 175; and Ohio Gov. John Kasich with less than 150.

Winning the nomination will require 1,237 delegates on the convention floor in Cleveland in July. The brash billionaire still needs to accelerate his pace of delegate-gathering to reach the 50-per-cent mark, otherwise he’ll remain vulnerable to a co-ordinated takedown effort in July.

The party establishment has already hinted at a plan to take him down on the second ballot — by rallying around an anti-Trump figure on the convention floor in what could be the first contested convention in decades.

Kasich promoted that approach. He won his home state Tuesday, delivering Trump’s sole defeat. He promised he would remain in the race until the confrontation four months from now in Cleveland.

“We are going to go all the way to Cleveland and secure the Republican nomination,” said Kasich, in a cheerful victory speech in tune with a campaign message more upbeat than that of other Republicans.

Rubio and Kasich had essentially reached an arrangement, as part of an effort to suppress Trump’s delegate totals: the Florida senator endorsed Kasich in Ohio and the Ohio governor did the same for Rubio in Florida.

The ruse worked in Ohio, not in Florida.

Rubio’s resignation will thrill Democrats who saw him as their biggest threat. Unlike any other Republican with the exception of Kasich, he consistently beat Hillary Clinton in hypothetical head-to-head matchups.

The rival closest to Trump is not participating in the pre-convention machinations. No. 2 delegate-holder Cruz warned it would cause chaos if party brass tried hand-picking a favourite.

Cruz said over the weekend: “That would be a disaster. The people would revolt. The only way to beat Donald Trump is beat him at the ballot box.”

A famous Republican strategist agreed there are no simple options, whether the party picks Trump or tries to block him. Karl Rove told Fox News over the weekend: “The party is likely to be bitterly divided almost no matter what the outcome.”

Allan Lichtman, a well-known electoral forecaster, said it would be nuts to try wresting the nomination from Trump, if he arrives at the Cleveland convention close to 50 per cent.

“I think that’s a fool’s errand,” said Lichtman, a history professor at American University.

“It’s going to rip the party apart and it may even lead to Donald Trump running a third-party campaign.”

As for the Democrats, Clinton extended her lead with big wins in Florida, Ohio and North Carolina, and held a smaller lead in Illinois. She was losing to Vermont Sen. Bernie Sanders in Missouri.