Thin films with low adhesion and large residual stresses may buckle and delaminate from their substrates. This delamination often results in oscillating patterns known as ‘telephone cords’. Other configurations can be observed as well, such as entangled networks of blisters. The present study aims at elucidating how these networks are generated through branching. A model coupling a geometrically non-linear plate model and a cohesive zone with mode dependent interfacial toughness is used. Previous work on the early stage delamination of initially circular blisters during interfacial crack front propagation are revisited and extended to the remote post-critical regime to capture front branching. We also build a partial phase diagram of buckling driven delamination morphologies. An intrinsic critical stress parameter is proposed which can be used to predict delamination morphology and to define ‘safe’ conditions where buckle propagation can be avoided. This critical stress also defines an intrinsic lengthscale which plays the role of a minimum nucleation size