Columbia (United States) (AFP) - Donald Trump and his rivals brawled on for the Republican presidential nomination Sunday as Hillary Clinton sailed toward "Super Tuesday," her White House hopes lofted by a blow-out win in South Carolina.

With just two days to go before the biggest showdown yet in the US presidential race, Clinton gained crucial momentum in the race for the Democratic nomination after crushing Bernie Sanders 73.5 to 26 percent.

"We got decimated," Sanders conceded in an interview on ABC's This Week show, acknowledging that the outpouring of African American support for Clinton exposed a costly weakness in his campaign.

On the Republican side, Trump's trailing rivals desperately tried to raise doubts among voters about the frontrunner's ability to beat Clinton in November.

Senator Ted Cruz suggested in an interview with ABC's "This Week" show that Mafia dealings could be hiding in Trump's tax returns, which the billionaire real estate developer has so far resisted releasing.

"There have been multiple media reports of Donald's dealings with the mob, the Mafia," Cruz said. "Maybe his tax returns will show that those business dealings are a lot more extensive than has been reported."

"We don't know," he added. "But the important point is ... in the general election, Hillary Clinton is going to shine a light on all of this. And Republican primary voters deserve to know."

- Trump's tax returns -

Trump has said he will not release his tax returns because they are being audited by the Internal Revenue Service.

"You can't tell anything from tax returns because you take deductions, massive deductions and lots of other things," he said on CNN's State of the Union Show.

Cruz also chided Trump for failing to categorically reject endorsements from white supremacist David Duke.

"Really sad.@realDonaldTrump you're better than this," Cruz tweeted.

Asked about the endorsement on CNN, Trump said he knew nothing about it. "You wouldn't want me to condemn a group that I know nothing about. I'd have to look," he said.

Story continues

At a news conference Friday, Trump appeared surprised by the endorsement. "David Duke endorsed me? I disavow," he said, without elaborating.

Polls show Trump, who picked up a key endorsement from New Jersey Governor Chris Christie, leading the Republican pack in most of the 11 Super Tuesday contests, but trailing Cruz in his home state of Texas, a top Super Tuesday prize with 155 delegates.

The conventional wisdom is that Trump's rivals -- Cruz, Senator Marco Rubio of Florida and Ohio Governor John Kasich -- must at least win their own states to remain in the running. Cruz will be the first to face that test, as Florida and Ohio vote later.

"There is no doubt that if Donald steamrolls through Super Tuesday, wins everywhere with big margins, that he may well be unstoppable," Cruz said on CBS's Face the Nation.

Kasich predicted that Trump would probably win all the Super Tuesday contests, but the governor said he intended to hang on in hopes Cruz and Rubio are knocked out first.

Retired neurosurgeon Ben Carson also has vowed to remain in the race, but support for his candidacy has fizzled.

With the stakes nearing a make-or-break point, Trump, Cruz and Rubio have viciously attacked each other with taunts, accusations and angry tweets that have given the Republican race a distinctly Darwinian flavor.

"Frankly, we're going to look back on this time and we're all going to shake our heads and say, did we really degrade the process of picking the leader of the free world?" said Kasich, who has generally refrained from joining the free-for-all.

- Redemption -

While the Republicans were hitting all the political talk shows Sunday, Hillary Clinton was quietly savoring her victory in South Carolina.

It was the former secretary of state's first decisive win of the campaign, after a nail-biter victory in Iowa, a thumping loss to Sanders in New Hampshire and then a five-point win in Nevada.

Exit polls in South Carolina showed African-Americans -- who represented 61 percent of all Democratic voters in the primary -- backed Clinton by a stunning 86 percent, more than had supported Obama eight years prior.

Clinton, who now leads in the national delegate count, assiduously courted black voters, partly by praising Obama and promising to build on his legacy.

South Carolina marked a "great test" for the coming votes in other southern states and showed that Clinton "can get a broad base of support of all demographics," her communications director Jennifer Palmieri told reporters, as the candidate shook hands and posed for selfies with supporters in Columbus, South Carolina Saturday night.

"We are going to compete for every vote in every state. We are not taking anything, and we are not taking anyone, for granted," Clinton said.

She also looked beyond her battle with Sanders, tweaking Trump, whose campaign slogan is "Make America Great Again."

"Despite what you hear, we don't need to make America great again. America has never stopped being great," she said, reading off a teleprompter.

The 11 states that hold Democratic nominating contests Tuesday will send a whopping 18 percent of the delegates to July's nominating convention in Philadelphia.