  This paper studies several aspects of symbolic ({\em i.e.}\ subshift) factors
of $\mathcal{S}$-adic subshifts of finite alphabet rank. First, we address a
problem raised in [DDPM20] about the topological rank of symbolic factors of
$\mathcal{S}$-adic subshifts and prove that this rank is at most the one of the
extension system, improving results from [E20] and [GH2020]. As a consequence
of our methods, we prove that finite topological rank systems are coalescent.
Second, we investigate the structure of fibers $\pi^{-1}(y)$ of factor maps
$\pi\colon(X,T)\to(Y,S)$ between minimal $\mathcal{S}$-adic subshifts of finite
alphabet rank and show that they have the same finite cardinality for all $y$
in a residual subset of $Y$. Finally, we prove that the number of symbolic
factors (up to conjugacy) of a fixed subshift of finite topological rank is
finite, thus extending Durand's similar theorem on linearly recurrent subshifts
[D00].

Dynamical Systems