where is the root user's home directory located on a mac os x file system
Home directory The Unix superuser has access to all directories on the filesystem, and hence can access home directories of all users. The superuser's home directory on older systems was /, but on many newer systems it is located at /root (Linux, BSD), or /var/root (Mac OS X).
Single user mode Unix-like operating systems provide single user mode functionality either through the System V-style runlevels, BSD-style boot-loader options, or other boot-time options.
macOS At macOS's core is a POSIX compliant operating system built on top of the XNU kernel, with standard Unix facilities available from the command line interface. Apple has released this family of software as a free and open source operating system named Darwin. On top of Darwin, Apple layered a number of components, including the Aqua interface and the Finder, to complete the GUI-based operating system which is macOS.[59]
Superuser In Unix-like computer OSes, root is the conventional name of the user who has all rights or permissions (to all files and programs) in all modes (single- or multi-user). Alternative names include baron in BeOS and avatar on some Unix variants.[2] BSD often provides a toor ("root" written backward) account in addition to a root account.[3] Regardless of the name, the superuser always has a user ID of 0. The root user can do many things an ordinary user cannot, such as changing the ownership of files and binding to network ports numbered below 1024.