  In the framework of the see-saw mechanism the normal hierarchy is favorable
for the neutrino mass spectrum. For this spectrum we present a detailed
calculation of the half-lives of neutrinoless double beta decay for several
nuclei of experimental interest. The half-lives are evaluated by considering
the most comprehensive nuclear matrix elements, which were obtained within the
renormalized QRPA by the Bratislava-Caltech-Tuebingen group. The dependence of
the half-lives on sin^2 theta_{13}$ and the lightest neutrino mass is studied.
We present also the results of the calculations of the half-lives of
neutrinoless double beta decay in the case of the inverted hierarchy of
neutrino masses.
