  We perform a series of two-dimensional magnetorotational core-collapse
simulations of Pop III stars. Changing the initial distributions of rotation
and magnetic fields prior to collapse in a parametric manner, we compute 19
models. By so doing, we systematically investigate how rotation and magnetic
fields affect the collapse dynamics and explore how the properties of the
black-hole formations and neutrino emissions could be affected. As for the
microphysics, we employ a realistic equation of state and approximate the
neutrino transfer by a multiflavour leakage scheme. With these computations, we
find that the jet-like explosions are obtained by the magnetodriven shock waves
if the initial magnetic field is as large as $10^{12}$ G. We point out that the
black-hole masses at the formation decrease with the initial field strength, on
the other hand, increase with the initial rotation rates. As for the neutrino
properties, we point out that the degree of the differential rotation plays an
important role to determine which species of the neutrino luminosity is more
dominant than the others. Furthermore, we find that the stronger magnetic
fields make the peak neutrino luminosities smaller, because the magnetic
pressure acts to halt the collapse in the central regions, leading to the
suppression of the releasable gravitational binding energies.
