The stellar mass range 8 less than or similar to M/M-circle dot less than or similar to 12 corresponds to the most massive asymptotic giant branch (AGB) stars and the most numerous massive stars. It is host to a variety of supernova (SN) progenitors and is therefore very important for galactic chemical evolution and stellar population studies. In this paper, we study the transition from super-AGB (SAGB) star to massive star and find that a propagating neon-oxygen-burning shell is common to both the most massive electron capture supernova (EC-SN) progenitors and the lowest mass iron-core-collapse supernova (FeCCSN) progenitors. Of the models that ignite neon-burning off-center, the 9.5 M-circle dot star would evolve to an FeCCSN after the neon-burning shell propagates to the center, as in previous studies. The neon-burning shell in the 8.8 M-circle dot model, however, fails to reach the center as the URCA process and an extended (0.6 M-circle dot) region of low Y-e (0.48) in the outer part of the core begin to dominate the late evolution; the model evolves to an EC-SN. This is the first study to follow the most massive EC-SN progenitors to collapse, representing an evolutionary path to EC-SN in addition to that from SAGB stars undergoing thermal pulses (TPs). We also present models of an 8.75 M-circle dot SAGB star through its entire TP phase until electron captures on Ne-20 begin at its center and of a 12 M-circle dot star up to the iron core collapse. We discuss key uncertainties and how the different pathways to collapse affect the pre-SN structure. Finally, we compare our results to the observed neutron star mass distribution.