KNOXVILLE, Tenn.—A nationwide search for head football coach? It’s almost a foreign concept at Tennessee.

Now that coach Phillip Fulmer has announced he’s stepping down at the university’s request at the end of this season, it’s reality for Tennessee athletic director Mike Hamilton. And Hamilton wrote in an e-mail late Monday night after Fulmer’s public announcement that the school is starting a national search immediately.

“We have a great university, world-class student-athletes, tremendous fans and first-class facilities,” he wrote. “As a result, we will attract some...

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