  The relations between the effective Majorana mass of the electron neutrino,
$m_{ee}$, responsible for neutrinoless double beta decay, and the neutrino
oscillation parameters are considered. We show that for any specific
oscillation pattern $m_{ee}$ can take any value (from zero to the existing
upper bound) for normal mass hierarchy and it can have a minimum for inverse
hierarchy. This means that oscillation experiments cannot fix in general
$m_{ee}$. Mass ranges for $m_{ee}$ can be predicted in terms of oscillation
parameters with additional assumptions about the level of degeneracy and the
type of hierarchy of the neutrino mass spectrum. These predictions for $m_{ee}$
are systematically studied in the specific schemes of neutrino mass and flavor
which explain the solar and atmospheric neutrino data. The contributions from
individual mass eigenstates in terms of oscillation parameters have been
quantified. We study the dependence of $m_{ee}$ on the non-oscillation
parameters: the overall scale of the neutrino mass and the relative mass
phases. We analyze how forthcoming oscillation experiments will improve the
predictions for $m_{ee}$. On the basis of these studies we evaluate the
discovery potential of future \znbb decay searches. The role \znbb decay
searches will play in the reconstruction of the neutrino mass spectrum is
clarified. The key scales of $m_{ee}$, which will lead to the discrimination
among various schemes are: $m_{ee} \sim 0.1$ eV and $m_{ee} \sim 0.005$ eV.
