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We assess the variance of the post-collapse evolution remnants of compact,massive, low-metallicity stars, under small changes in the degrees of rotationand magnetic field of selected pre-supernova cores. These stellar models arecommonly considered progenitors of long gamma-ray bursts. The fate of theproto-neutron star (PNS) formed after collapse, whose mass may continuouslygrow due to accretion, critically depends on the poloidal magnetic fieldstrength at bounce. Should the poloidal magnetic field be sufficiently weak,the PNS collapses to a black hole (BH) within a few seconds. Models on thisevolutionary track contain promising collapsar engines. Poloidal magneticfields smooth over large radial scales (e.g. dipolar fields) or slightlyaugmented with respect to the original pre-supernova core yield long-lastingPNSs. In these models, BH formation is avoided or staved off for a long time,hence, they may produce proto-magnetars (PMs). Some of our PM candidates havebeen run for $\lesssim 10\,$s after core bounce, but they have not entered theKelvin-Helmholtz phase yet. Among these models, some display episodic events ofspin-down during which we find properties broadly compatible with thetheoretical expectations for PMs ($M_{PNS} \approx 1.85\,M_\odot -2.5\,M_\odot$, $\bar{P}_{PNS} \approx 1.5 - 4\,$ms, and $b^{\rm surf}_{PNS}\lesssim 10^{15}\,$G) and their very collimated supernova ejecta has nearlyreached the stellar surface with (still growing) explosion energies $\gtrsim2\times 10^{51}\,$erg.

Magnetorotational core collapse of possible GRB progenitors. II. Formation of protomagnetars and collapsars