Michael,
Thanks for the quick reply. Yes, you described what I'm seeing exactly.

" Your original curve objects that you drew initially and gave as input into the Network command are also still around, those are separate objects from the surface that was created or the surface edges that are sub-objects of the surface."

Do I need to keep the original curve objects? For example, I might be modeling a car fender and what to attach a new curved surface to one to the one I just created.