  We show that uniformly finite homology of products of $n$ trees vanishes in
all degrees except degree $n$, where it is infinite dimensional. Our method is
geometric and applies to several large scale homology theories, including
almost equivariant homology and controlled coarse homology. As an application
we determine group homology with $\ell_{\infty}$-coefficients of lattices in
products of trees. We also show a characterization of amenability in terms of
1-homology and construct aperiodic tilings using higher homology.
