  Based on recent results from three-dimensional supernova simulations and
semi-analytical parametrised models, we develop analytical prescriptions for
the dependence of the mass of neutron stars and black holes and the natal
kicks, if any, on the pre-supernova carbon-oxygen core and helium shell masses.
Our recipes are probabilistic rather than deterministic in order to account for
the intrinsic stochasticity of stellar evolution and supernovae. We anticipate
that these recipes will be particularly useful for rapid population synthesis,
and we illustrate their application to distributions of remnant masses and
kicks for a population of single stars.
