A system doing exactly this is NIS. Formely called YP. This is ONE documentation page:
http://www.yolinux.com/TUTORIALS/NIS.html. But there are many more if you google for "NIS howto".
It is very simple, does the job and is able to mount a home directory. It was designed for that. You have to make sure that users across all machines have the same uid:gid for a username:groupname.
The other option is LDAP. But IMHO more complicated. I never used it.
jlinkels