It has recently been observed that the SIR distributions of a variety of cellular network models and transmission techniques look very similar in shape. As a result, they are well approximated by a simple horizontal shift of the distribution of the most tractable model, the Poisson point process. This paper makes a first step towards explaining this remarkable property by showing that the asymptotics of the SIR distribution near 0 and near infinity can only differ by a constant. © 2015 IEEE.