We study the strength of the binding of 4d and 5d transition metals on a graphene sheet in the limit of high-coverage using first principles density functional theory. A database of the binding energies is presented. Our results show that the elements with low or near-half occupation of the d shell bind strongest to the graphene sheet. We find a transfer of electrons from the transition metal to the graphene sheet; the charge transfer decreases with increasing d shell occupation. Motivated by the strong binding to Hf we also study the binding of graphene to the Hf rich surface of HfO2. The predicted binding energy of −0.18 eV per C atom when coupled with the existing integration of HfO2 into Si-based CMOS devices suggests a new route to integrating graphene with silicon, allowing for an integration of graphene-based nanoelectronic components into existing silicon-based technology.