This paper is a study of the optimal geometric layout of schemes for distributing hot water uniformly over an area. Constrained are the amount of insulation material, the volume of all the pipes, and the amount of pipe wall material. Unknown are the distribution of insulation over all the links of the network, and the configuration of the network itself. The main focus is on how the geometric configuration may be selected in the pursuit of maximized global performance, and how closely a non-optimal configuration performs to the highest level. Three global optimization criteria are considered, and they all yield similar results with respect to the distribution of insulation: the maximization of the temperature of the hot water received by the farthest user. the minimization of the total heat loss of the network, and the maximization of the delivery temperature averaged over all the users. Three configurations are optimized: (a) an area covered by a coiled stream, where all the users are aligned on the same stream, (b) a sequence of tree-shaped flows on square areas in which each area construct is made up of four smaller area constructs, and (c) a sequence of tree-shaped flows where each area construct is made up of two smaller area constructs. It is shown that the tree-shaped designs (b) and (c) outperform consistently and significantly the coiled stream design (a). The tree designs obtained by pairing (c) are better than the square tree constructs (b) and, in addition, they deliver water at the same temperature to all the users spread over the territory. The optimized tree networks (b) and (c) approach the same high level of global performance as their complexity increases. Optimized tree-shaped flow designs are robust.