An elderly Cuban-American man sat in a lawn chair outside Miami city hall last week, surrounded by Donald Trump lawn signs. He wore a denim shirt and a ball cap emblazoned with the phrase "Make America great again," Mr. Trump's campaign slogan.

He didn't want to be interviewed, saying he mistrusted journalists, as many Trump supporters do. But he explained that he admired the New York developer's business acumen and supported his strong stance against illegal immigration.

Then he went to his car – a Lexus sedan – and took a Trump flyer out of the trunk.

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"He's a good man," he said, handing the document to a reporter.

Similar scenes are common across Florida. In a sign of just how unpredictable this race for the Republican presidential nomination has become, Mr. Trump now finds himself with a respectable following among the large Cuban-American population in this crucial battleground state.

As Floridians vote in their primary Tuesday, the phenomenon continues to puzzle observers – not only because Mr. Trump has made disparaging remarks about Hispanics, but because, extraordinarily, there are two Cuban-American candidates in the race. While one of them, Ted Cruz, was raised in Texas and has little profile in Florida, Marco Rubio is a Miami native who has held office in the Sunshine State for more than a decade.

Mr. Trump's support among Mr. Rubio's base is just one sign of the favourite son's faltering campaign. Tuesday's primary is considered do-or-die for the first-term senator, who will probably drop out if he fails to secure Florida's 99 winner-take-all delegates.

And Mr. Rubio trails badly in every local poll. A Quinnipiac University survey released Monday shows Mr. Trump supported by 46 per cent of likely Republican primary voters, against 22 per cent for Mr. Rubio.

In Miami-Dade County, where the Latino population is so predominant that non-Hispanic whites are referred to as Anglos, Mr. Rubio might have been expected to have an overwhelming advantage. He speaks movingly about his family's struggle to establish itself in the United States and promises to undo the Obama administration's rapprochement with the Castro regime, which many Cuban-Americans fled.

But a range of factors appear likely to split the Cuban vote. Many in the community were supporters of Jeb Bush, a popular former Florida governor, and even though he dropped out of the race weeks ago, the state's long early-voting period makes it likely that Mr. Bush will garner thousands of votes cast when he was still a candidate.

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Mr. Trump, meanwhile, has his own sources of support in Cuban enclaves such as Hialeah and West Tampa. Reports in the New York Times, Associated Press and Miami Herald have noted the counterintuitive trend among Cuban-Americans.

Pat Santangelo, a former Democratic candidate for state representative, said that many Miami Cubans take a hard line on immigration. The older generation, especially, think of themselves as political exiles, rather than mere immigrants, and support Mr. Trump's plan to build a wall along the Mexican border.

"They like the wall," Mr. Santangelo said. "My wife: Trump supporter."

Since 1966, at the height of the Cold War, Cubans immigrating to the United States have received special dispensation, receiving permanent residency after a year on American soil.

"Cubans here have a very different understanding of immigration," said Daniel Smith, a professor of political science at the University of Florida.

Others in the community support Mr. Trump for the same stylistic traits that have struck a chord across the country. Tomas Regalado, the mayor of Miami, said that Cuban constituents occasionally approach him with avowals of support for the populist billionaire.

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"I have heard people support Trump saying, 'He's tough,'" said Mr. Regalado. "I've heard people supporting Trump saying, 'It's time we finally had someone who told the truth.'"

Mr. Regalado said he was personally disturbed by Mr. Trump's candidacy, especially his racially charged rhetoric. Like what is likely a solid majority of Cuban-Americans, he backs Mr. Rubio.

But he acknowledges an unaccountable core of Trump voters in the community he calls home – a reality that perplexes and frustrates him in equal measure. An elderly Cuban man told the mayor he'd be voting Trump recently.

"I said 'Why?'" Mr. Regalado recalled. "And he said, 'Because Trump tells the truth.' And I said,'Well, give me an example.' And he said, 'Well, he tells the truth.'"

"People cannot explain his support."