  We devise a generalization of tree approximation that generates conforming
meshes, i.e., meshes with a particular structure like edge-to-edge
triangulations. A key feature of this generalization is that the choices of the
cells to be subdivided are affected by that particular structure. As main
result, we prove near best approximation with respect to conforming meshes,
independent of constants like the completion constant for newest-vertex
bisection. Numerical experiments complement the theoretical results and
indicate better approximation properties than previous approaches.
