Voters in 12 states solidified the standing of Donald J. Trump and Hillary Clinton as the front-runners in their parties’ nominating contests on Tuesday. But while the results seemed to clarify the Democratic race, the Republicans face some uncertainty in the weeks ahead as Mr. Trump’s rivals seek a way forward.

Here are some takeaways from the biggest day of voting so far in the 2016 election:

Trump Can Win All Over

He took seven of 11 states — Alabama, Arkansas, Georgia, Massachusetts, Tennessee, Vermont and Virginia — and broke the age-old political dictum that a gilded New Yorker could not win in the Deep South. He has now won a majority of the first 15 nominating contests, a point he will raise every time his critics, rivals and opponents suggest he has to be stopped.

With Super Tuesday behind him, Mr. Trump was looking ahead to the general election at a news conference at his Mar-a-Lago property in Florida. The candidate, best known for scathing insults and divisive language, made his best attempt at magnanimity. “Believe me, I’m a unifier,” Mr. Trump said.

Trump’s Rivals Are Still Looking for a Path

Before Mr. Trump’s victory lap, Senator Ted Cruz of Texas and Senator Marco Rubio of Florida made the case — to voters, but also to the party — that they offered the best chance to stop Mr. Trump. Mr. Cruz used his victories, in Alaska, Oklahoma and Texas, to argue that the party should rally around him. Mr. Rubio, 44, is likely to cling to his first win, in Minnesota — a swing state where the electorate is hospitable to the young, fresh-faced Hispanic senator — as he heads toward the primary in his home state of Florida on March 15, where Mr. Trump is leading in the polls.