Write Work flow
User Access set up(for new and existing)
Monitor performance and control outages
Back up data as and when required
Purge old data
Addition Customized fields for modules as per needs of projects
Normally once a project is set up, QC admin gets request to add users , add fields or modify them and then user permissions comes in. creating a project is the key after that as long as you keep track of license and stay on top of things life is easy.
TDAdmin is the obvious "QC admin" role, which encompasses all of the PROJECT-BASED setup and configuration mentioned above but the other element of QC administration is Site Administration which seems to be often overlooked
From a QC persepctive:
Quality Center patching
License management: Average concurrency, Peak concurrency
Backup & Restore regimes and policy
Archiving of old/unused projects
These are all very application-specific tasks that your infrastructure/Ops/server management team may not even be aware of, let alone consider in scope for themselves.
..which brings me to a final crucial QC Admin job:
maintaining effective working relationships with the Server adminstration team and DBA's !