We investigated the wear formation during a single-asperity sliding against a rigid substrate using molecular dynamics simulations. Two distinct wear mechanisms were observed: low-load atomic wear (isolated debris atoms or clusters) and high-load plastic wear (collective debris formation from plastic flow). The atomic wear rate depends on the normal stress exponentially, in agreement with the mechanically assisted bond-rupture theory. However, the plastic wear rate exhibits linear dependency on the normal stress. It was found that the asperity-substrate adhesion reduces the critical normal stress for the atomic-to-plastic wear transition, suppressing the atomic wear mode. Finally, a wear mechanism map of atomic/plastic wear was constructed in the domain of normal stress and adhesion, which is consistent with existing simulation and experimental results. This wear map could resolve the recent controversy on whether Archard׳s linear law is applicable for low-load tip wear. •Both atomic and plastic wear were observed in tip wear MD simulations.•Tip wear formula was obtained for atomic wear and plastic wear.•High adhesion suppresses atomic wear in single-asperity sliding.•A new stress-adhesion wear mechanism map is proposed.