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We study branch structures in Grigorchuk-Gupta-Sidki groups (GGS-groups) overprimary trees, that is, regular rooted trees of degree $p^n$ for a prime $p$.Apart from a small set of exceptions for $p=2$, we prove that all these groupsare weakly regular branch over $G''$. Furthermore, in most cases they areactually regular branch over $\gamma_3(G)$. This is a significant extension ofpreviously known results regarding periodic GGS-groups over primary trees andgeneral GGS-groups in the case $n=1$. We also show that, as in the case $n=1$,a GGS-group generated by a constant vector is not branch.

GGS-groups over primary trees: Branch structures