  We introduce two definitions of $G$-equivariant partitions of a finite
$G$-set, both of which yield $G$-equivariant partition complexes. By
considering suitable notions of equivariant trees, we show that $G$-equivariant
partitions and $G$-trees are $G$-homotopy equivalent, generalizing existing
results for the non-equivariant setting. Along the way, we develop equivariant
versions of Quillen's Theorems A and B, which are of independent interest.
