The full potential of graphene in integrated circuits can only be realized with a reliable ultrathin high-κ top-gate dielectric. Here, we report the first statistical analysis of the breakdown characteristics of dielectrics on graphene, which allows the simultaneous optimization of gate capacitance and the key parameters that describe large-area uniformity and dielectric strength. In particular, vertically heterogeneous and laterally homogeneous Al2O3 and HfO2 stacks grown via atomic-layer deposition and seeded by a molecularly thin perylene-3,4,9,10-tetracarboxylic dianhydride organic monolayer exhibit high uniformities (Weibull shape parameter β > 25) and large breakdown strengths (Weibull scale parameter, E BD > 7 MV/cm) that are comparable to control dielectrics grown on Si substrates.