As a retired educator I've watched the evolution of home schooling with interest over the past thirty years.  In fact as a principal-teacher in a small village school I once purchased the state's high school Science curriculum for home-schooling so to not burden my students with my limited scientific expertise, and it was excellent.  Most students I've known who've been home-schooled have had exceptional knowledge, occasionally limited in interesting ways.  One bright teen-aged young lady who used to watch our children would have detailed discussions with me @ Edgar Allen Poe and the causes of the Civil War, but didn't know who Princess Diana was.  On the other hand I've also witnessed home-schooled children literally hanging out in public libraries, unsupervised, socializing and horsing around with each other.  Ultimately it comes down to the parent(s) and their dedication to the curriculum guides and learning activities of their children.