The transfer process of graphene onto the surface of oxide substrates is well known. However, for many devices, we require high quality oxide thin films on the surface of graphene. This step is not understood. It is not clear why the oxide should adopt the epitaxy of the underlying oxide layer when it is deposited on graphene where there is no lattice match. To date there has been no explanation or suggestion of mechanisms which clarify this step. Here we show a mechanism, supported by first principles simulation and structural characterisation results, for the growth of oxide thin films on graphene. We describe the growth of epitaxial SrTiO3 (STO) thin films on a graphene and show that local defects in the graphene layer (e.g. grain boundaries) act as bridge-pillar spots that enable the epitaxial growth of STO thin films on the surface of the graphene layer. This study, and in particular the suggestion of a mechanism for epitaxial growth of oxides on graphene, offers new directions to exploit the development of oxide/graphene multilayer structures and devices.