We present an analysis of inclusive Ωc0 baryon production and decays in 230.5fb-1 of data recorded with the BABAR detector. Ωc0 baryons are reconstructed in four final states (Ω-π+, Ω-π+π0, Ω-π+π+π-, Ξ-K-π+π+) and the corresponding ratios of branching fractions are measured. We also measure the momentum spectrum in the e+e- center-of-mass frame. From the spectrum, we observe Ωc0 production from B decays and in cc̄ events, and extract the two rates of production. © 2007 The American Physical Society.