In what primary did Romney win a majority of the votes?
According to the Wall Street Journal, it was the Texas primary that put him over the top (May 29).
That wasn’t my question. In most of the primaries, he didn’t get a majority of the vote. He “won” with a plurality, meaning most GOP voters wanted somebody else.
Your question is phrased in the singular, but the answer is very much in the plural. Romney got over half in a couple of dozen states, at least, although the higher percentages were mostly in the states voting later. In the end, Romney got 51.5% of the total primary popular vote, so it's not fair to say he won by a mere plurality. Lots of numbers here.
The rules were actually fairer this time around. Most states were not winner-take-all, so there was room for less popular candidates to collect delegates. For instance, I voted for Newt in Massachusetts on March 6. When I checked the results and found he got only 4.7%, I realized I should have voted for Santorum or Paul, each of whom came much closer to the 15% threshold to take a delegate away from Mittens, who got almost 72%.
Here's a map showing how the counties sorted out:
Orange is Romney's color. The darker the shade, the higher the percentage. E.g. check out Utah (LOL!).