I think you mean literal successor. It's descended from NeXT's codebase. Mac OS X 10.0 was basically NeXTSTEP 6 with Apple logos, Carbon and a Mac OS 9 VM.

There's a "ship of theseus" problem with this idea. There's enough different about OS X (different kernel and BSD base, different display server, different driver stack) that I think it's fair to describe it as a separate OS, yet clearly a lot _is_ directly taken from NS, especially the ObjC/application layer stuff. The waters are further muddled by the existence of Rhapsody and OS X Server 1.0, which are much more clearly "NeXTSTEP 6 with Apple logos, Carbon and a Mac OS 9 VM". I don't think anyone outside the original OS X development team really knows just how much code was kept vs scrapped for the start of OS X development. Given that NS/OS was based on USL-encumbered BSD, it seems likely to me that nothing from the original NS kernel was kept for that, at a minimum.