We consider the number of users associating with each base station in a cellular network. Extending and unifying the characterizations for certain settings available in the literature, we derive a result that is asymptotic in the strength of the shadowing, yet otherwise universally valid: it holds for every network geometry and shadowing distribution. We then illustrate how this result provides excellent representations in various classes of networks and with realistic shadowing strengths, evidencing broad applicability.

This work was supported by Project TEC2015-66228-P (MINECO/FEDER, UE), by the European Research Council under the H2020 Framework Programme/ERC grant agreement 694974, and by the U.S. NSF through award CCF 1525904.