  Let $G$ be a locally compact second countable group equipped with an
admissible non-degenerate Borel probability measure $\mu$. We generalize the
notion of $\mu$-stationary systems to $\mu$-stationary $G$-factor maps $\pi:
(X,\nu)\to (Y,\eta)$. For these stationary relations between dynamical systems,
we provide a structure theorem, which generalizes the structure theorem of
Furstenberg-Glasner. Furthermore, we show the existence and uniqueness of a
relative version of the Poisson boundary in this setup.
