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The problem of optimum design of tree-shaped power distribution networks with respect to the voltage drop effect is addressed in this paper. An approach for the width adjustment of the power lines supplying the circuit's major functional blocks is formulated, so that the network occupies the minimum possible area under specific voltage drop constraints at all blocks. The optimization approach is based on precise maximum current estimates derived by statistical means from recent advances in the field of extreme value theory. Experimental tests include the design of power grid for a choice of different topologies and voltage drop tolerances in a typical benchmark circuit.