AbstractIn this paper we review the behavior of growing stellar degenerate cores. It is shown that ONeMg white dwarfs and cold CO white dwarfs can collapse to form a neutron star. This collapse is completely silent since the total amount of radioactive elements that are expelled is very small and a burst of γ-rays is never produced. In the case of an explosion (always carbonoxygen cores), the outcome fits quite well the observed properties of Type Ia supernovae. Nevertheless, the light curves

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... d the velocities measured at maximum are very homogeneous and the diversity introduced by igniting at different densities is not enough to account for the most extreme cases observed. It is also shown that a promising way out of this problem could be the He-induced detonation of white dwarfs with different masses. Finally, we outline that the location of the border line which separetes explosion from collapse strongly depends on the input physics adopted.