We study the adhesion between an elastomer of cross-link index, P , and a flat solid surface where polymer chains of polymerisation index, N , have been end-grafted. To understand the adhesive feature of such a system, one has to study both the origin of the grafted layer interdigitation with the network and the end-grafted chain extraction out of the elastomer when it separates from the solid surface. Both aspects are addressed here. We develop an analytical model that allows one to predict a critical surface grafting density, sigma*similar or equal to P-1/10/N-3/5 , beyond which only the thermal fluctuations allow the layer to interdigitate with the elastomer. A review of the possible mechanisms of chain extraction is proposed.