Abstract-The outage analysis of networks with randomly distributed nodes has been mostly restricted to the case of Poisson networks, where the node locations form a homogeneous Poisson point process. In this paper, we show that in great generality, the outage probability, as a function of the density of interfering nodes η, approaches γη κ as η goes to zero, where γ and κ are the spatial contention and the interference scaling exponent, respectively. Interestingly, κ is restricted to a small range of possible values: 1 ≤ κ ≤ α/2 for a path loss exponent α. We also prove that for ALOHA, κ = 1 irrespective of the point process properties, and we demonstrate how the upper bound κ = α/2 can be achieved.