  We establish the existence of solutions to a weakly-coupled competitive
system of polyharmonic equations in R^N which are invariant under a group of
conformal diffeomorphisms, and study the behavior of least energy solutions as
the coupling parameters tend to $-\infty$. We show that the supports of the
limiting profiles of their components are pairwise disjoint smooth domains and
solve a nonlinear optimal partition problem of R^N. We give a detailed
description of the shape of these domains.
