  We study an ergodic theorem for disjoint C*-dynamical systems, where
disjointness here is a noncommutative version of the concept introduced by
Furstenberg for classical dynamical systems. This is applied to W*-dynamical
systems. We also consider specific examples of disjoint C*-dynamical and
W*-dynamical systems, including for actions of other groups than $\mathbb{Z}$.
Unique ergodicity and unique ergodicity relative to the fixed point algebra are
closely related to disjointness, and are used to give examples of disjoint
C*-dynamical systems.
