  We address a question of Grigorchuk by providing both a system of recursive
formulas and an asymptotic result for the portrait growth of the first
Grigorchuk group. The results are obtained through analysis of some features of
the branching subgroup structure of the group. More generally, we provide
recursive formulas for the portrait growth of any finitely generated,
contracting, regular branch group, based on the coset decomposition of the
groups that are higher in the branching subgroup structure in terms of the
lower subgroups. Using the same general approach we fully describe the portrait
growth for all non-symmetric GGS-groups and for the Apollonian group.
