Direct products of free groups in $\mathrm{A}\mathrm{u}\mathrm{t}(F_N)$

We give a complete description of the embeddings of direct products of nonabelian free groups into $\mathrm{A}\mathrm{u}\mathrm{t}(F_N)$ and $\mathrm{O}\mathrm{u}\mathrm{t}(F_N)$ when the number of direct factors is maximal. To achieve this, we prove that the image of each such embedding has a canonical fixed point of a particular type in the boundary of Outer space.