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We explore the final fates of massive intermediate-mass stars by computingdetailed stellar models from the zero age main sequence until near the end ofthe thermally pulsing phase. These super-AGB and massive AGB star models are inthe mass range between 5.0 and 10.0 Msun for metallicities spanning the rangeZ=0.02-0.0001. We probe the mass limits M_up, M_n and M_mass, the minimummasses for the onset of carbon burning, the formation of a neutron star, andthe iron core-collapse supernovae respectively, to constrain the whitedwarf/electron-capture supernova boundary. We provide a theoretical initial tofinal mass relation for the massive and ultra-massive white dwarfs and specifythe mass range for the occurrence of hybrid CO(Ne) white dwarfs. We predictelectron-capture supernova (EC-SN) rates for lower metallicities which aresignificantly lower than existing values from parametric studies in theliterature. We conclude the EC-SN channel (for single stars and with thecritical assumption being the choice of mass-loss rate) is very narrow ininitial mass, at most approximately 0.2 Msun. This implies that between ~ 2-5per cent of all gravitational collapse supernova are EC-SNe in the metallicityrange Z=0.02 to 0.0001. With our choice for mass-loss prescription and computedcore growth rates we find, within our metallicity range, that CO cores cannotgrow sufficiently massive to undergo a Type 1.5 SN explosion.

Super and massive AGB stars - IV. Final fates - Initial to final mass relation