Transferred graphene provides a promising III-nitride semiconductor epitaxial platform for fabricating multifunctional devices beyond the limitation of conventional substrates. Despite its tremendous fundamental and technological importance, it remains an open question on which kind of epitaxy is preferred for single-crystal III-nitrides. Popular answers to this include the remote epitaxy where the III-nitride/graphene interface is coupled by nonchemical bonds, and the quasi-van der Waals epitaxy (quasi-vdWe) where the interface is mainly coupled by covalent bonds. Here, we show the preferred one on wet-transferred graphene is quasi-vdWe. Using aluminum nitride (AlN), a strong polar III-nitride, as an example, we demonstrate that the remote interaction from the graphene/AlN template can inhibit out-of-plane lattice inversion other than in-plane lattice twist of the nuclei, resulting in a polycrystalline AlN film. In contrast, quasi-vdWe always leads to single-crystal film. By answering this long-standing controversy, this work could facilitate the development of III-nitride semiconductor devices on two-dimensional materials such as graphene.