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A key problem in wireless networking is how to choose a link activation schedule and associated powers in concert with routing decisions to optimize throughput. Back-pressure control policies are optimal in this context, but the underlying power control problem is non-convex. Back-pressure power control (BPPC) was recently shown to be NP-hard, yet amenable to successive convex approximation strategies that deliver manifold improvements in end-to-end throughput relative to the prior art in wireless networking. A drawback is that existing implementations are centralized, whereas practical power control has to be distributed across the network. This paper fills this gap by developing a distributed version of the core step of successive convex approximation of the BPPC problem, building upon the Alternating Direction Method of Multipliers (ADMoM). The resulting protocol enjoys favorable properties relative to dual decomposition - based implementations, and allows tight approximation of the BPPC objective in all interference regimes. Judicious simulations reveal that the proposed algorithm matches the performance of its centralized counterpart, as well as pertinent trade-offs in terms of the design parameters.