It appears that the home directory of the root user is indeed set to /var/root on OSX.
On linux it's usually /root/
I guess you can take the value of the environment variable $SUDO_USER if the application was run as root through sudo and use that to derive the home directory.
[[[NSProcessInfo processInfo] environment] objectForKey:@"SUDO_USER"]
Remember that files created by the application when it's run as root will be owned by user root by default.
Also, maybe you'd like to consider why you are even running this application as root in the first place. Maybe there is a better way to do it.