  In this article we analyze the nuclear matrix elements (NME) of the
neutrinoless double beta decays of the nuclei 48-Ca, 76-Ge, 82-Se, 124-Sn,
130-Te and 136-Xe in the framework of the Interacting Shell Model (ISM). We
study the relative value of the different contributions to them, such as higher
order terms in the nuclear current, finite nuclear size effects and short range
correlations, as well as their evolution with the maximum seniority permitted
in the wave functions. We discuss also the build-up of the NME's as a function
of the distance between the decaying neutrons. We calculate the decays to final
0+ first excited states and find that these decays are at least 25 times more
supressed with respect to the ground state to ground state transition.
