Donald Trump, the real estate magnate and reality television star who has said Mexican immigrants are rapists and has called for banning all Muslims from the U.S., won the Republican primary in the pivotal state of Indiana on Tuesday night. Sen. Ted Cruz (R-Texas), his most serious remaining challenger, dropped out . Trump is now the presumptive nominee of the Republican Party .

The Republican presidential primary is a race for delegates, not votes, and for months, Trump's opponents had held out hope that they would win enough delegates to deny him a majority on the first ballot at the July convention. Now, after last week's stronger-than-expected showing in Pennsylvania , Trump looked likely to wrap up the nomination earlier than his foes had feared. His Indiana win comes on a day dominated by Trump's charge that his GOP rival's father was involved in the assassination of President John F. Kennedy. Seriously. That happened.

Trump didn't need Indiana to keep him on track for an outright victory, but his win on Tuesday made the ultimate outcome all but certain. Trump had nearly 1,000 delegates going into Tuesday. With his strong showing in Indiana, he should win the vast majority of that state's 57 delegates and draw within 200 delegates of the 1,237 he needs to secure the nomination.

In California and New Jersey, the largest remaining states, polling shows Trump ahead by more than 20 points. If those numbers hold -- which they almost certainly will, given that Cruz has dropped out -- he'll win all of New Jersey's 51 delegates and the vast majority of California's 172.

The delegate math and Cruz's decision confirmed what most Republican voters have already accepted. Trump now has the support of more than half of Republicans nationwide , according to HuffPost Pollster's average, with twice the backing of Sen. Ted Cruz (R-Texas). And even before Indiana voted, 91 percent believed Trump would win the nomination, according to a CNN/ORC survey . PredictWise, which forecasts political events based on political betting markets, gave Trump an 88 percent chance of winning a majority of delegates as of Tuesday morning , up 28 points since this time last month.

[Read More: Ted Cruz Threw Everything But The Kitchen Sink At Donald Trump. It Still Didn't Work .]

As Trump moved closer to the nomination, Republicans have warmed to the idea of having him as their standard-bearer. Republicans' opinions of Trump, while still notably mixed, have ticked upward in the past month, according to polling from Gallup . Views of Cruz, meanwhile, have plummeted for the first time into negative territory.