The units of departments, research centers, etc. listed on eScholarship are those which have been created and are maintained by the departments themselves. If there is no department listed, papers from that department may be in the general "postprints" section for that university, for example UC San Diego Postprints.
Departments which are interested in starting and maintaining a unit should consult the "Request a new unit" article and/or get in touch with the eScholarship team to begin setting up a unit.