In a previously presented proof-of-principle study, we established a parameterized spherically symmetric explosion method (PUSH) that can reproduce many features of core-collapse supernovae (CCSN). The present paper goes beyond a specific application that is able to reproduce observational properties of SN1987A and performs a systematic study of an extensive set of nonrotating, solar metallicity stellar progenitor models in the mass range from 10.8 to 120M_{sun}_. This includes the transition from neutron stars to black holes as the final result of the collapse of massive stars, and the relation of the latter to supernovae, possibly faint supernovae, and failed supernovae. We discuss the explosion properties of all models and predict remnant mass distributions within this approach. The present paper provides the basis for extended nucleosynthesis predictions in a forthcoming paper to be employed in galactic evolution models.