To what extent is the clerical work (i.e. amending flight plans, logging, etc.) of a center air traffic controller now automated?
... Do center controllers have to manually amend every flight plan now that ERAM is fully implemented? To what extent is the process automated?


Yup. ERAM does not take away tasks from controllers, it just makes them easier.


  For controllers, ERAM provides a user-friendly interface with customizable displays. Trajectory modeling is more accurate, allowing maximum airspace use, better conflict detection and improved decision making. — FAA


Controllers still fill out and pass on flight strips. Physical flight strips are being phased out by the Advanced Electronic Flight Strips (AEFS), for center controllers and all the other facilities.


  AEFS replaces traditional paper flight strips, and manual tracking of incoming and outgoing flights, with an electronic flight data display. The system can be updated through a touch screen or mouse. Controllers no longer need to physically carry a flight strip across the control room. A simple swipe of the finger sends the data to another station. This allows the controller to stay engaged with the traffic at all times. — FAA


AEFS will eventually be replaced by the Terminal Flight Data Manager (TFDM).

It wouldn't surprise me if they print out those flight strips, just in case.



Source: FAA