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Another possible contender, real estate magnate Donald Trump, was a no-show, but an aide, Michael Cohen, created a stir anyway when he arrived unexpectedly in Des Moines aboard the billionaire’s personal jet — emblazoned with the word “Trump” on the side — to meet with an array of party officials.

Mr. Cohen said he hadn’t been sent by Mr. Trump, but that he was in the state to gauge interest in a Trump candidacy.