The decomposition of the Solar system abundances of heavy isotopes into their s- and r- components plays a key role in our understanding of the corresponding nuclear processes and the physics and evolution of their astrophysical sites. We present a new method for determining the s- and r- components of the Solar system abundances, fully consistent with our current understanding of stellar nucleosynthesis and galactic chemical evolution. The method is based on a study of the evolution of the solar neighborhood with a state-of-the-art 1-zone model, using recent yields of low and intermediate mass stars as well as of massive rotating stars. We compare our results with previous studies and we provide tables with the isotopic and elemental contributions of the s- and r-processes to the Solar system composition.