What happens to a child with an enlarged heart as he grows up?

Depends: If this is a cardiomyopathy it will get worse. There are several causes and you should ask the doctor who found the enlarged heart.

Find cause: All fat kids and all very athletic kids have enlarged hearts by the old standards from the 1950's when most folks were thinner and sedentary. Be sure you know the cause before drawing any conclusions! if it's hypertrophic cardiomyopathy, aortic stenosis, or hypertension or you've been given the name of another disease, follow it very closely.

Need to know cause: An "enlarged" heart is not always a problem. As others have answered, athletes have "enlarged" hearts. On the other hand, all sorts of heart conditions can lead to an enlarged heart; some may be relatively minor while others are life-threatening. Please discuss this issue with a pediatrician/pediatric cardiologist as the answer depends on the specific cause.