The aim is to focus on the development of partially premixed combustion after diffusion flame quenching. To this end, the quenching of a planar two-dimensional diffusion flame is studied by using numerical simulation. A flame hole is obtained by submitting the reaction zone to a high strain and scalar dissipation rate resulting from the interaction between vorticity and upstream triple flame which stabilizes the diffusion dame. The set of control parameters is chosen so that effects of unsteadiness are not expected during quenching, thus, extinction appears for a scalar dissipation rate that is well predicted by one-dimensional flamelet theory. Backward propagating edge dames develop at both extremities of the quenched zone, whereas the combustion regime evolves from diffusion to partially premixed. From the results and the transport equation for a partially premixed fraction, a cross-scalar dissipation rate is introduced as a direct measure of the extent of partial premixing in non-premixed systems. For unity Lewis number, it is shown that the maximum burning rate measured in a one-dimensional planar stoichiometric premixed flame may be used as a reference for a diffusion flame close to extinction and also later when edge flames and triple flames are formed. Finally, the simulations suggest that the scalar dissipation rate controlling the growth of the flame hole is lower than the one that should be applied to first quench the flame.