The possibility that a dominant fraction of the cosmic rays above the ankle is due to the single source Centaurus~A is discussed. We focus on the properties of the source spectrum and composition required to reproduce the observations, showing that the nuclei are strongly suppressed for $E > 10Z$~EeV, either by a rigidity-dependent source cutoff or by the photodisintegration interactions with the cosmic microwave background at the giant dipole resonance. The very mild attenuation effects taking place at lower energies imply that the secondary nuclei produced in photodisintegration processes during propagation from this nearby source provide a small contribution. Given the moderate anisotropies observed, the deflections in extragalactic and Galactic magnetic fields should play a crucial role. The diffusion in extragalactic fields as well as the finite source lifetime significantly affect the shape of the observed spectrum. The cosmic-ray flux at tens of EeV is dominated by the CNO component, being actually better reproduced by a mixture of C and O nuclei rather than by just N, while heavier nuclei become dominant above 70~EeV. The cosmic ray flux at a few EeV should mostly result from a more isotropic light component associated with a population of extragalactic sources. The inclusion of the subdominant contribution of heavy nuclei from the Galactic component helps to reproduce the observations around 1~EeV.