The question of how to scale the mobility gradient of polymer chains near a substrate in supported ultrathin polymer films is a great challenge. In this paper, a mobility gradient of poly(ethylene terephthalate) (PET) chains near a substrate is characterized by cold crystallization. We found that either decreasing the PET film thickness or increasing the absorbed layer thickness consistently reveals three characteristic film thicknesses, which are all linearly dependent on the adsorbed layer thickness. At the first thickness, the low-temperature peak of the top surface crystallization starts to shift toward the high temperature peak of the bulk-like polymer crystallization; at the second thickness, it arrives there; and at the third thickness, crystallization is completely suppressed. The three kinds of film thicknesses characterize the depth profile of the local dynamics, reflecting the long-range effects of the substrate, which could be scaled by the thickness of the adsorbed layer.