10:05 p.m. ET

After Trump's primary win, the Empire State building turns red:





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9:46 p.m. ET

Donald Trump thanked his supporters in New York on Tuesday night and delivered a stern warning to those in the Republican establishment who may try to block his path to the nomination.

Republican presidential candidate Donald Trump speaks at his New York presidential primary night rally in Manhattan, New York, U.S., April 19, 2016. REUTERS

"It's really nice to win the delegates with the votes," he said. "Nobody should be given delegates, which is a ticket to victory but not a fair ticket."

Should a candidate secure the GOP nomination at the Republican National Convention without the popular vote to back it up, "the poeple aren't going to stand for it," he said. "It's a system that's rigged."

9:36 p.m. ET

A review of the CBS News exit polling shows that Donald Trump's win in New York on Tuesday night was big and broad.

He won the support of both men and women, college grads and those without a college degree.

Some of Trump's strongest support came from voters who were looking for a candidate who would bring needed change (Trump 68 percent, Kasich 19 percent, Cruz 13 percent) and those who were looking for someone who would tell it like it is (Trump 89 percent, Kasich 9 percent, Cruz 2 percent). He also won the backing of eight in 10 voters who want the next president to be from outside of politics.

Trump benefited from the smaller share of the electorate who call themselves very conservative. Just 23 percent of New York Republican voters identified as very conservative, among the lowest percentage in the states so far. These voters have often backed Cruz.

Trump is also seen as electable in November against Hillary Clinton. Fifty-six percent say he has the best chance of beating her in November, followed by Kasich (21 percent) and Cruz (15 percent).

Looking ahead, New York Republican voters are more concerned or scared about a potential Cruz presidency (six in 10 Republican voters say that) than either Trump (39 percent) or Kasich (47 percent). By comparison, in Wisconsin, 38 percent of Republican primary voters said they would be scared of what Trump would do if elected president, but fewer New Yorkers are scared of such a prospect. Just about a quarter say they would be scared of what Trump would do if elected president.

9 p.m. ET

Republican front-runner Donald Trump will win the New York primary, CBS News projects. The billionaire businessman is on his way to winning most of the 95 delegates at stake tonight.

Trump is running strong in Long Island and the Westchester suburbs.

Trump is getting widespread support across demographic groups, CBS News exit polling shows. He is winning the support of men, women, and is seen as the candidate with the best chance of beating Hillary Clinton.

As he has throughout this campaign, Trump is winning the support of those who want a candidate who can bring change. He wins the backing of 68 percent of those voters, while Cruz and Kasich split the rest at 15 percent each.

Looking ahead to November, Republican voters express more concern about Cruz being elected president than they do about Kasich or Trump. About a quarter of GOP New Yorkers are scared about a Trump presidency -- but that figure was 38 percent in Wisconsin.

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5:30 p.m. ET

More updates from the CBS News exit polling:

67 percent of Republican primary voters say that they are very worried about the direction of the nation's economy.

61 percent of Republican primary voters say that illegal immigrants working in the U.S. should be offered a chance to apply for legal status; 34 percent say they should be deported.

61 percent support a temporary ban on Muslims who are not U.S. citizens entering the country; 35 percent are opposed to a ban.

5:15 p.m. ET

New York Republicans are casting their ballots in the 2016 primary Tuesday, choosing from Donald Trump, Ted Cruz or John Kasich. A big win in the Empire State could put front-runner Donald Trump back on track -- albeit a narrow one -- to eventually clinch the GOP nomination.

Polls are open in New York City and many surrounding counties from 6 a.m. to 9 p.m. ET, and from noon to 9 p.m. everywhere else in the state.

The economy it the top issue for Republican voters in New York, CBS News exit polling shows. While 37 percent said it's the economy, another 27 percent said terrorism is the most important issue. Another 24 percent said government spending, and 8 percent named immigration.

There's some division on views of Wall Street among Republican voters. Fifty-one percent say Wall Street hurts the U.S. economy, while 46 percent say it helps it.

Bringing needed change is the candidate quality that mattered most to Republican primary voters, with 35 percent saying so. Another 28 percent said they're primarily looking for a candidate who shares their values, while 26 percent they primarily wants a candidate who "tells it like it is." Eight percent said they're mostly looking for a candidate who can win in November.

As we've seen in earlier primaries, most Republican primary voters in New York are unhappy with the way the federal government is working, including 36 percent who are angry. And more than six in 10 looking for an outsider as the next president rather than someone with political experience.

Polls out of the state suggest Trump could score big on Tuesday: The recent CBS News Battleground Tracker shows that he wins more support in his home state of New York than his two GOP competitors combined: Trump has 54 percent compared with 21 percent for Cruz and 19 percent for Kasich.

New York offers a total of 95 delegates for the GOP candidates: 14 statewide delegates are allocated proportionally, unless a candidate wins at least 50 percent of the vote -- then that candidate takes all 14. Another 81 delegates are split among the state's 27 congressional districts. If a candidate wins more than 50 percent in a district, he takes home all three of the district's delegates. If no one crosses that threshold, the winner takes home two and the second-place finisher (if he wins more than 20 percent) gets one.

Heading into the New York primary, according to the CBS News estimate, Trump has 755 delegates, Cruz has 554 and Kasich has 143. At this point, it's impossible for Kasich to win the 1,237 delegates needed to win the nomination outright, and it's unlikely Cruz will. Consequently, they're focused largely on ensuring that Trump doesn't reach 1,237, either.

It's possible Trump could score a major victory in New York and still fail to reach 1,237. However, if he does win by a wide margin, it make certain that no other candidate will be able to.

If no candidate gets a majority of delegates ahead of the convention, seven in 10 Republican New Yorkers say the candidate with the most votes should be the nominee, according to the exit polling. A quarter think the one the delegates who think would be the best candidate should be the nominee. More than half of Republican voters in New York say the campaign has divided their party, rather than energized it.