  We establish several classification results for compact extensions of tracial
$W^*$-dynamical systems and for relatively independent joinings thereof for
actions of arbitrary discrete groups. We use these results to answer a question
of Austin, Eisner, and Tao and some questions raised by Duvenhage and King.
Moreover, combining our results with an earlier classification of weakly mixing
extensions by Popa, we can derive non-commutative Furstenberg-Zimmer type
dichotomies on the $L^2$-level. Although in general an adequate generalization
of the Furstenberg-Zimmer tower of intermediate compact extensions doesn't seem
possible in the von Neumann algebraic framework, we show that there always
exists a non-commutative analogue of the finer Host-Kra-Ziegler tower for any
ergodic action of a countable abelian group.
