The fragmentation behaviour of a thin brittle coating attached to a ductile substrate subjected to equibiaxial quasi-static in-plane tension is studied. The experimentally observed cracking patterns are related to repetitively branching coating cracks. The fragmentation process is modelled by the rate equation approach. It is established that fragmentation by branching cracks leads to a qualitatively different fragment distribution compared to binary fragmentation. The fragmentation model is applied to identify crack branching and coating/substrate stress transfer parameters.