We calculate nuclear matrix elements (NME) of neutrinoless double beta decay (0νββ) in four different candidate nuclei ( 76 Ge, 82 Se, 100 Mo, 130 Te) within the quasiparticle random phase approximation (QRPA) and its uncertainties. We assume (up to) four coexisting mechanisms for 0ν2β decay, mediated by light Majorana neutrino exchange (ν), heavy Majorana neutrino exchange (N ), R-parity breaking supersymmetry ( / R), and squark-neutrino (q), interfering either constructively or destructively with each other. We find that, unfortunately, current NME uncertainties appear to prevent a robust determination of the relative contribution of each mechanism to the decay amplitude, even assuming accurate measurements of decay lifetimes. The near-degeneracy of 0νββ mechanisms is analyzed with simple algebraic techniques, which do not involve assumptions about the statistical distribution of errors. We discuss implications of such degeneracy on prospective searches for absolute neutrino masses.