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In this article, we consider joint optimization of user association and resource allocation in three tier HetNets. We formulate the objective of minimizing the resources required to clear a given set of files, as a linear program. We show that the optimal user association is determined by a rate-biasing rule, where a bias value is associated with each BS. We show that each rate-bias value crucially only takes values from a finite set which we characterize. We present a complete analytical solution along with new structural results. Using these results, we present efficient distributed algorithms for optimal control of three tier HetNets. The method involves a 1D search for a resource variable at the macro-level, and 2D search at the pico-level for a resource variable and a bias value. We apply our results to a variety of hierarchical network examples.