We investigate elastic-plastic adhesive wear via a continuum variational phase-field approach. The model seamlessly captures the transition from perfectly brittle, over quasi-brittle to elastic-plastic wear regimes, as the ductility of the contacting material increases. Simulation results highlight the existence of a critical condition that morphological features and material ductility need to satisfy for the adhesive junction to detach a wear debris. We propose a new criterion to discriminate between non-critical and critical asperity contacts, where the former produce negligible wear while the latter lead to significant debris formation.