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The final stages of the evolution of electron--degenerate ONe cores,resulting from carbon burning in ``heavy weight'' intermediate--mass stars ($8M_{\sun}\la M \la 11 M_{\sun}$) and growing in mass, either from carbon burningin a shell or from accretion of matter in a close binary system, are examinedin the light of their detailed chemical composition. In particular, we havemodelled the evolution taking into account the abundances of the followingminor nuclear species, which result from the previous evolutionary history:$^{12}$C, $^{23}$Na, $^{24}$Mg, and $^{25}$Mg. Both $^{23}$Na and $^{25}$Mggive rise to Urca processes, which are found to be unimportant for the finaloutcome of the evolution. $^{24}$Mg was formerly considered a major componentof ONe cores (hence called ONeMg cores), but updated evolutionary calculationsin this mass range have severely reduced its abundance. Nevertheless, we haveparameterized it and we have found that the minimum amount of $^{24}$Mgrequired to produce NeO burning at moderate densities is $\sim 23%$, a valueexceedingly high in the light of recent evolutionary models. Finally, we havedetermined that models with relatively small abundances of unburnt carbon($X(^{12}$C)$\sim 0.015$) could be a channel to explosion at low to moderatedensity ($\sim 1\times 10^9$ g cm$^{-3}$). This is clearly below the currentestimate for the explosion/collapse threshold and would have interestingconsequences.Comment: 8 pages, 6 figures, to appear in Astronomy and Astrophysic

The gravitational collapse of ONe electron-degenerate cores and white dwarfs: The role of $^\mathsf{24}$Mg and $^\mathsf{12}$C revisited