WASHINGTON — Donald Trump jetted to Atlanta, Marco Rubio flew to Tennessee and Arkansas, while Ted Cruz touted his strength in his home state of Texas.

The day after South Carolina elevated three Republican candidates — and a Nevada victory sent relief through Hillary Clinton’s campaign — the presidential contest entered a new phase of campaigning in scattered states that can best be reached by airplanes instead of buses.

A dozen states are scheduled to host nominating contests on Super Tuesday, just eight days away, when the South is prepared to flex its muscle in American politics with the power to go a long way toward settling both nominating contests. On the same day, a handful of northern states, including Massachusetts, will also vote in contests that Senator Bernie Sanders of Vermont and Governor John Kasich of Ohio hope will keep their candidacies alive.

This new terrain will open both presidential primaries to a far more diverse group of voters. It will force the campaigns to prioritize where to spend their time, and it could reward the better-funded candidates who can afford to air television ads in multiple markets across states.

“Last night was truly the beginning of the real Republican primary,’’ Senator Marco Rubio of Florida said Sunday morning on CNN. “I think the race last night was reset.’’

On the Republican side, the next set of delegate-rich states offers a test of each candidate’s strengths. Rubio on Sunday began trying to consolidate top donors, supporters, and surrogates now up for grabs after former Florida governor Jeb Bush dropped out of the race Saturday night.

For the Democrats, Clinton is shifting to more comfortable territory in states with large African-American populations, who are likely to bolster her efforts to gain control of the race after a significant threat from Sanders.

On Saturday, after Clinton’s victory speech in a ballroom at the Caesars Palace casino, she jetted to Texas. That state, with 222 delegates up for grabs, is the Super Tuesday prize.

“If the month of March is good for Clinton, which it’s set up to be as long as she keeps her foot on the gas pedal, she can wrap this up sooner rather than later,’’ said Mary Anne Marsh, a Boston-based Democratic strategist who is not working for either campaign.

Clinton racked up support among African-American voters in Nevada, according to entrance polls there. This bodes well for her prospects in South Carolina, Alabama, and Georgia.

The returns from Nevada also showed Clinton winning in Hispanic areas in Clark County by big numbers, casting doubt on entrance polls that suggested Sanders managed to boost his following among these voters.

The real test of Sanders’ strength among that population comes March 1, when Texas and Colorado — two places with larger Hispanic populations — are among the 11 states where Democrats will hold contests.

But first, there’s the Democrats’ South Carolina primary on Saturday. Sanders visited a black Baptist church in West Columbia on Sunday morning. Polls have never shown his message resonating there, and it’s unclear how much time he’ll spend in the state over the next week.

On Monday, the Vermont senator turns to a more friendly Super Tuesday state. He’ll host a rally at the University of Massachusetts Amherst, touching down in a state where he’s leading in one recent poll.

On the Republican side, Trump enters the crucial next week with numerous advantages, including that Kasich is still a force in the race who could prevent Rubio from consolidating more mainstream Republican support.

“There’s not been a good history of people taking on Trump,’’ said Chip Saltsman, a Tennessee-based Republican consultant who ran Mike Huckabee’s 2008 and 2016 campaigns. “The long and windy road to the White House has been littered with bodies of people who thought they could take on Trump.’’

Strikingly, the questions around the Republican field are the same ones that have been there for six months. There’s still consternation around Trump, and his enduring support. Rubio has tremendous potential but has not won a state yet. And Cruz has yet to prove he can move beyond his evangelical base.

The South has been Cruz’s firewall, but that wall is showing some signs of structural damage. For months Cruz has emphasized his strength among evangelical Christians. That coalition helped him in Iowa, but he is struggling to broaden his appeal, and exit polls in South Carolina showed Trump did better than Cruz among evangelicals.

Cruz started the month with $13.6 million in his campaign account, more than any other candidate, according to filings released on Saturday. Rubio had $5 million, while Kasich had $1.5 million. Trump had $1.6 million, but the billionaire who is self-funding his campaign could add more at any time.

Most of the focus during the first three states has been an effort at grabbing momentum, beating expectations, and doing enough to justify staying in the race. But now candidates must begin to keep an eye on amassing delegates.

Among Republicans, Trump is dominating with 67 delegates, followed by Cruz with 11, Rubio with 10, Kasich with five, and Ben Carson with three.

For Republicans, whose Nevada caucus will take place Tuesday, 595 delegates are at stake March 1, with 80 percent of those coming from Southern states. The biggest haul of the day is the 155 delegates in Texas, which is Cruz’s home state.

Some Republicans are hoping that Bush’s exit will allow Rubio to consolidate establishment support. But even assuming that Rubio would have inherited all of Bush’s voters in the first three states, it would not have been enough for him to win any of them.

Kasich, the only governor left in the race, is banking on northern and Midwestern states carrying him forward.

On the day that South Carolina primary voters headed to the polls, Kasich was in Burlington, Vt., and Worcester, Mass.

His main goal is holding on until Michigan votes on March 8, and then he is hoping to score big winner-take-all victories on March 15 in Illinois and his home state, Ohio.

Matt Viser can be reached at matt.viser@globe.com. Annie Linskey can be reached at annie.linskey@globe.com. Follow her on Twitter @annielinskey.