I and gaining an ever expanding list of of core.mountd.12009999475 type files in my root directory? What are these? Can I just delete them?
What causes them to be created?
That's called a core file. When a process crashes (in this case, mountd) the system makes a copy of the process's memory space (core) and saves it to disk for later analysis by an administrator (you).
You can safely delete them. To disable them, use
coreadm -d process.
(Note: That's literally the word "process", don't put the name of a process there.)
Read more about core files at http://developers.sun.com/solaris/articles/manage_core_dump.html