  We consider the action of Anosov subgroups of a semi-simple Lie group on the
associated flag manifolds. A systematic approach to construct cocompact domains
of discontinuity for this action was given by Kapovich, Leeb and Porti in
arXiv:1306.3837. For $\Delta$-Anosov representations, we prove that every
cocompact domain of discontinuity arises from this construction, up to a few
exceptions in low rank. Then we compute which flag manifolds admit these
domains and, in some cases, the number of domains. We also find a new
compactification for locally symmetric spaces arising from maximal
representations into $\mathrm{Sp}(4n+2, \mathbb{R})$.
