  Bestvina introduced a $\mathcal{Z}$-structure for a group $G$ to generalize
the boundary of a CAT(0) or hyperbolic group. A refinement of this notion,
introduced by Farrell and Lafont, includes a $G$-equivariance requirement, and
is known as an $\mathcal{E}\mathcal{Z}$-structure. In this paper, we show that
fundamental groups of graphs of nonpositively curved Riemannian $n$-manifolds
admit $\mathcal{Z}$-structures and graphs of negatively curved or flat
$n$-manifolds admit $\mathcal{E}\mathcal{Z}$-structures. This generalizes a
recent result of the first two authors with Tirel, which put
$\mathcal{E}\mathcal{Z}$-structures on Baumslag-Solitar groups and
$\mathcal{Z}$-structures on generalized Baumslag-Solitar groups.
