Optimal channel networks (OCNs) are dendritic structures obtained by minimizing the local and global rates of energy dissipation in a continuously fed (in space and time) plane aggregation system reminiscent, and based on the properties, of the planform of three-dimensional natural drainage networks. Geomorphological and fractal properties of OCNs are known from earlier studies by the authors. This paper explores further the structures derived by optimization of energy dissipation rates. Optimality of subnetworks and of basin shapes is investigated as a by-product of competition for drainage. A new perspective on the possible prediction of the width function of a basin network, and hence of its hydrologic response, is obtained by exploiting OCN techniques, requiring only the definition of the outer boundaries of the basin. The interplay between hillslope processes and the development of drainage networks is addressed, aiming at the relative role and the mutual interrelations of geology and optimal organization in the structure of mature river basins. Also addressed is the issue of multiscaling and multifractality in the spatial organization of the network. It is concluded that OCN approaches provide a comprehensive framework for the study of the morphology of geophysical structures.