The most widely applied resource allocation strategy is to balance, or equalize, the total workload assigned to each resource. In mobile multi-agent systems, this principle directly leads to equitable partitioning policies in which (i) the workspace is divided into subregions of equal measure, (ii) there is a bijective correspondence between agents and subregions, and (iii) each agent is responsible for service requests originating within its own subregion. In this paper, we provide the first distributed algorithm that provably allows m agents to converge to an equitable partition of the workspace, from any initial configuration, i.e., globally. Our approach is related to the classic Lloyd algorithm, and provides novel insights into the properties of power diagrams. Simulation results are presented and discussed.