Unlike in classical Rayleigh-Bénard convection, boundary conditions in the Earth's atmosphere typically impose a stable mean density stratification. Convection is instead driven by local internal heating due to the condensation of water vapour. We consider this process in the simple moist convection model named Rainy-Bénard, in which any condensed water is removed from the system on a rapid time scale to mimic precipitation. The asymmetry of the buoyancy driving in the model leads to a state of narrow, moist updrafts surrounded by wide regions of unsaturated air, as observed in previous studies of other moist convection systems. Through three-dimensional direct numerical simulations of the Rainy-Bénard system, we identify how a Rayleigh number based on the moist static energy controls the strength and spacing of the updrafts. We further analyse the process of self-aggregation in the system, which leads to the spontaneous breaking of azimuthal symmetry in large updrafts.