The transfer process of graphene onto the surface of ferroelectric thin films is well known. However, for many devices, is required high quality oxide thin films to be grown 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 present a mechanism, supported by first principles simulation and structural characterisation results, for the growth of oxide ferroelectric 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. In this study, SrTiO3 layers with thicknesses varying from 10nm to 100 nm were deposited using pulsed laser deposition. To measure its electrical properties, the STO film was covered with a 50 nm Au layer using dc magnetron sputtering; and MIM capacitor structures were formed with photo-lithography followed by ion-milling. The surface of the STO film was analyzed using AFM, while its crystal structure was examined by x-ray, SEM and TEM. Results of the electrical measurements carried out within a temperature range of 77K up to 100oC will be presented.