Summary: The present paper is the third article (see Zbl 1101.76350 for Part II) in a three-part series on anisotropic mesh adaptation and its application to two- and three-dimensional, structured and unstructured meshes. This third paper concerns the application of the full adaptation methodology to 2-D unstructured meshes, including all four mesh modification strategies presented in Part I (Zbl 0981.76052), i.e. refinement/coarsening, edge swapping and node movement. The mesh adaptation procedure is validated through a careful monitoring of a single adaptation step and of the solution-adaptation loop. Independence from the initial mesh and from the flow solver is illustrated. The efficiency of the overall methodology is investigated on relevant laminar and turbulent flow benchmarks.