  This paper studies several aspects of symbolic 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
$\pi\colon(X,T)\to(Y,T)$ 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.
