  We investigate the explosion of stars with zero-age main-sequence masses
between 20 and 35 solar masses and varying degrees of rotation and magnetic
fields including ones commonly considered progenitors of gamma-ray bursts
(GRBs). The simulations, combining special relativistic magnetohydrodynamics, a
general relativistic approximate gravitational potential, and two-moment
neutrino transport, demonstrate the viability of different scenarios for the
post-bounce evolution. Having formed a highly massive proto-neutron star (PNS),
several models launch successful explosions, either by the standard supernova
mechanism based on neutrino heating and hydrodynamic instabilities or by
magnetorotational processes. It is, however, quite common for the PNS to
collapse to a black hole (BH) within a few seconds. Others might produce
proto-magnetar-driven explosions. We explore several ways to describe the
different explosion mechanisms. The competition between the timescales for
advection of gas through the gain layer and heating by neutrinos provides an
approximate explanation for models with insignificant magnetic fields. The
fidelity of this explosion criterion in the case of rapid rotation can be
improved by accounting for the strong deviations from spherical symmetry and
mixing between pole and equator. We furthermore study an alternative
description including the ram pressure of the gas falling through the shock.
Magnetically driven explosions tend to arise from a strongly magnetised region
around the polar axis. In these cases, the onset of the explosion corresponds
to the equality between the advection timescale and the timescale for the
propagation of Alfv\'en waves through the gain layer.
