  (short version) - A model for GRMHD disk outflows with neutrino-driven mass
ejection is developed,and employed to calculate the structure of the outflow in
the sub-slow magnetosonic region and the mass loading of the outflow, under
conditions anticipated in the central engines of gamma-ray bursts. The
dependence of the mass flux on the conditions in the disk, on magnetic field
geometry, and on other factors is carefully examined for a range of neutrino
luminosities expected in hyperaccreting black holes. The fraction of neutrino
luminosity that is being converted to kinetic energy flux is shown to be a
sensitive function of the effective neutrino temperature at the flow injection
point, and the shape of magnetic field lines in the sub-slow region, but is
practically independent of the strength of poloidal and toroidal magnetic
fields. We conclude that magnetic launching of ultra-relativistic polar
outflows from the innermost parts of the disk is in principle possible provided
the neutrino luminosity is sufficiently low, $L_\nu\simlt10^{52}$ erg s$^{-1}$
or so. The conditions found to be optimal for the launching of an
ultra-relativistic jet are also the conditions favorable for large
neutron-to-proton ratio in the disk.
