  We introduce the notion of dynamically marked rational maps. We study
sequences of analytic conjugacy classes of rational maps which diverge in
moduli space. In particular, we are interested in the notion of rescaling
limits introduced by Jan Kiwi. In order to deal with those, we introduce the
notion of dynamical covers between trees of spheres for which a periodic sphere
corresponds to a rescaling limit. We then recover results of Jan Kiwi regarding
rescaling limits.
