Assembling arrays of ordered nanowires is a key objective for many of their potential applications. However, a lack of understanding and control of the nanowires' growth mechanisms limits their thorough development. In this work, an appealing new path towards self-organized epitaxial nanowire networks produced by high-throughput solution methods is reported. Two requisites are identified to generate the nanowires: a thermodynamic driving force for an unrestricted elongated equilibrium island shape, and a very fast effective coarsening rate. These requirements are met in anisotropically strained Ce(1-x)Gd(x)O(2-y) nanowires with the (011) orientation grown on the (001) surface of LaAlO(3) substrates. Nanowires with aspect ratios above ≈100 oriented along two mutually orthogonal axes are obtained leading to labyrinthine networks. A very fast effective nanowire growth rate (≈60 nm min(-1)) for ex-situ thermally annealed nanostructures derives from simultaneous kinetic processes occurring in a branched network. Ostwald ripening and anisotropic dynamic coalescence, both promoted by strain-driven attractive nanowire interaction, and rapid recrystallization, enabled by fast atomic diffusion associated with a high concentration of oxygen vacancies, contribute to such an effective growth rate. This bottom-up approach to self-organized nanowire growth has a wide potential for many materials and functionalities.