A bstract The matching relations in the unpolarized and polarized variable flavor number scheme at three-loop order are presented in the single-mass case. They describe the process of massive quarks becoming light at large virtualities Q 2 . In this framework, heavy-quark parton distributions can be defined. Numerical results are presented on the matching relations in the case of the single-mass variable flavor number scheme for the light parton, charm and bottom quark distributions. These relat