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To provide a high quality power delivery system, the power needs to be regulated on-chip with ultra-small locally distributed power efficient converters. Historically, power efficient switching converters require large physical area, while compact linear power supplies exhibit high power conversion losses, which are not ideal for on-chip integration. To exploit the advantages of existing power supplies, a heterogeneous power delivery system is proposed. The power efficiency of the system is shown to be a strong function of the on-chip distribution of the power supplies. The optimal power distribution system with minimum power losses is determined by exhaustively comparing the power efficiency for all possible power supply topologies. A heterogeneous system with ten on-chip voltage domains and an optimal power distribution network has been evaluated, demonstrating up to 93% power efficiency. A power efficient clustering of the on-chip power supplies with linear computational complexity is also proposed. Heterogeneous power delivery systems with up to 100 on-chip voltage domains have been evaluated with power supplies distributed with linear computational complexity. A maximum 1.5% drop in power efficiency from the optimal solution has been observed, yielding a near optimal and high fidelity power supply distribution system.