New Delhi, June 20 -- When Illumination founder and chief executive Chris Meledandri earlier this month received a star on the Hollywood Walk of Fame, he wondered how many visitors it will have.

"In years to come, as people walk down Hollywood Boulevard, they'll come across my star," he said to the assembled crowd. "And unless they're related to me, they'll ask: 'Who the hell was that guy?'"

Yet at a time of perpetual upheaval in Hollywood, the unflashy Meledandri has created and shaped one of Hollywood's most consistent blockbuster-making operations. Family-friendly movies are fueling the box office like never before, and Illumination is at the forefront of it.

Since Illumination's first release, 2010's "Despicable Me," the animation ...