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The CBS News Battleground Tracker poll shows that Donald Trump keeps a large lead in South Carolina, bolstered by support from conservatives and also from evangelical voters, who make up a large share of the electorate here.

Ted Cruz is in second place, but well behind Trump. Cruz has the support of those who consider themselves very conservative, but trails Trump among all conservatives as well as moderates.

John Kasich has gotten a little bounce out of his surprisingly strong showing in New Hampshire, but he may be limited here by the fact that evangelical voters are not as strongly in support of him as non-evangelicals.

For Trump voters, who have been relatively steadfast in their support over the last few months, the percentage who say they've firmly decided on Trump has increased. Trump's lead among evangelicals is up from January, and he has widened his lead among conservatives, too.

In a contest marked by divisions among so-called "insiders" and "outsiders," South Carolina Republicans show a strong preference for campaigns running as the latter, and this poll helps illustrate why. By four to one, South Carolina Republicans describe the "establishment" as a bad thing, and few describe it as a group that knows how to get things done.

On the metric of being "prepared" to be president, Trump and Cruz do well, and Jeb Bush and John Kasich do relatively well, but Marco Rubio trails in this regard, suggesting that last week's debate in New Hampshire may have had an impact.

Hillary Clinton keeps her large lead in South Carolina, which has narrowed only slightly from last month, and she is bolstered by strong support from the African American voters who comprise most of the Democratic electorate here.

Bernie Sanders leads among white voters and younger voters, continuing the campaign dynamics we saw in Iowa and New Hampshire, but in South Carolina that is not enough to bring him close.

Some of those other factors are also in play here. Sanders leads Clinton on being seen as honest and trustworthy, though here, a majority see both candidates as honest, so the effect is not as pronounced. And Clinton leads on preparedness for the Presidency, also echoing themes her campaign stressed in previous states.

The CBS News 2016 Battleground Tracker is a panel study based on interviews conducted on the internet of registered voters in Florida, Georgia, Iowa, New Hampshire, South Carolina, and Texas. The poll was conducted by YouGov, an online polling organization.

The first wave was fielded between September 3-10, 2015, with 4860 respondents, and the second wave fieldwork was completed between October 15-22, 2015, with 3952 respondents and the third wave between November 15-19, 2015. The fourth wave was fielded between December 13-17, 2015. The majority of the 2nd-4th wave respondents are recontacted panelists. The first 4 waves consist of interviews in Iowa, New Hampshire, and South Carolina only. The fifth wave added new interviews in Florida, Georgia, and Texas, and was completed between January 17-21, 2016. The sixth wave was fielded only in South Carolina, with interviews completed February 10-12, 2016.

Respondents were selected from YouGovs and two other online panels. These are "opt-in" panels which are open for anyone to join. However, YouGov also randomly selected persons from voter registration lists who had previously voted in primary elections and contacted them by phone. A total of 22 517 registered voters were contacted by phone and the YouGov sample includes 1753 phone recruits.