- Dryland landscapes self-organize to form various patterns of vegetation patchiness. Two major classes of patterns can be distinguished: regular patterns with characteristic length scales and scale-free patterns. The latter form under conditions of global competition over the water resource. In this paper we show that the asymptotic dynamics of scale-free vegetation patterns involve patch coarsening similar to Ostwald ripening in two-phase mixtures. We demonstrate it numerically, using a spatially explicit model for water-limited vegetation, and further study it by drawing an analogy to an activator-inhibitor system that shares many properties with the vegetation system. The ecological implications of patch coarsening may not be highly significant due to the long time scales involved. The reported results, however, raise an interesting pattern formation question associated with the incompatibility of mechanisms that stabilize vegetation spots and the condition of global competition.