  We consider the question of determining the scaling of the $n^2$-dimensional
balanced unicast and the $n 2^n$-dimensional balanced multicast capacity
regions of a wireless network with $n$ nodes placed uniformly at random in a
square region of area $n$ and communicating over Gaussian fading channels. We
identify this scaling of both the balanced unicast and multicast capacity
regions in terms of $\Theta(n)$, out of $2^n$ total possible, cuts. These cuts
only depend on the geometry of the locations of the source nodes and their
destination nodes and the traffic demands between them, and thus can be readily
evaluated. Our results are constructive and provide optimal (in the scaling
sense) communication schemes.
