  The exact solutions of the complete Dirac equation for fermions moving in
ideal Aharonov-Bohm rings are used for deriving the exact expressions of the
relativistic partial currents. It is show that as in the non-relativistic case
these currents can be related to the derivative of the fermion energy with
respect to the flux parameter. A specific relativistic effect is the saturation
of the partial currents for high values of the total angular momentum. Based on
this property, the total relativistic persistent current at $T=0$ is evaluated
giving its analytical expression and showing how this depend on the ring
parameters.
