  We study Schreier dynamical systems associated with a vast family of groups
that hosts many known examples of groups of intermediate growth. We are
interested in the orbital graphs for the actions of these groups on $d-$regular
rooted trees and on their boundaries, viewed as topological spaces or as spaces
with measure. They form interesting families of finitely ramified graphs, and
we study their combinatorics, their isomorphism classes and their geometric
properties, such as growth and the number of ends.
