Donald Trump seemingly had a tough week. He faced an onslaught of attacks from his competitors, Mitt Romney and outside groups. He suffered an upset loss in Maine and nearly lost Louisiana and Kentucky, two states where he was expected to fare well. Polls showed him slipping nationally.

But the results on Tuesday suggest that Mr. Trump remains in a strong position, at least as long as the field remains divided. He carried Michigan and Mississippi by healthy margins and later won in Hawaii.

His opposition did not become as strong as he might have feared after Ted Cruz’s performance on Saturday, either.

The results look a lot more like the race we had on Super Tuesday: a double-digit advantage for Mr. Trump, who holds an edge in a three-way race, rather than the close race suggested by new national polls.