We highlight in a model independent way the dependence of the effective Majorana mass parameter, relevant for neutrinoless double beta decay, on the CP phases of the PMNS matrix, using the most recent neutrino data including the cosmological WMAP measurement. We perform our analysis with three active neutrino flavours in the context of three kinds of mass spectra: quasi-degenerate, normal hierarchical and inverted hierarchical. If a neutrinoless double beta decay experiment records a positive signal, then assuming that Majorana masses of light neutrinos are responsible for it, we show how it might be possible to discriminate between the three kinds of spectra. PACS number(s): 14.60.Pq, 23.40.-s.The importance of looking for neutrinoless double beta decay (0νββ) lies in the fact that, if observed, it would establish a violation of the total lepton number, which is otherwise a conserved quantum number in the standard model. Any nonvanishing amplitude for this decay may be inferred as a signal for an effective Majorana mass of the electron neutrino. This way it is sensitive to some kind of an absolute mass of the neutrino, contrary to the oscillation experiments, which can fix only the neutrino mass squared differences. An evidence for this decay has recently been claimed on the basis of results from Heidelberg-Moscow experiments [1]. This claim has been criticized by authors in [2], which has subsequently been followed by a reply to the criticism made [3]. In any case, the currently running NEMO3 experiment [4] and future [5] (Majorana, EXO, CUORICINO, CUORE, GENIUS) (0νββ) experiments would either confirm this evidence or would put a stronger bound on the amplitude of this decay. The rate of (0νββ) is proportional to the square of the (ee)-element of the neutrino mass matrix, often called the effective mass parameter m ee . This parameter depends on the absolute neutrino masses, the solar and CHOOZ mixing angles, and two CP phases. A detailed discussion of the dependence of m ee on different parameters may be found, e.g., in [6,7].The purpose of this short note is to highlight in a model independent way the dependence of m ee on the CP phases, using the most recent oscillation data on mass square splittings and mixing angles [8,9,10,11,12,13], as well as the recent cosmological bound from WMAP on the sum of all neutrino masses [14] in conjunction with data from 2dF galaxy redshift survey (2dFGRS) [15]. We base our 1 analysis on the three possible kinds of mass spectra: quasi-degenerate, hierarchical and inverted hierarchical, in the context of three neutrino generations. The (0νββ) experiment in a sense serves to distinguish between the spectra: due to the present sensitivity, its observation in the ongoing (0νββ) experiment, as it would turn out, would only establish a nearly degenerate mass spectrum.We stress at this point that even though the (0νββ) amplitude does depend on the CP phases, this decay does not correspond to a manifest CP-violating phenomenon. The rate of this decay is indeed affected by ...