  The source of cosmic gamma-ray bursts (hereafter GRBs) is usually believed to
be a stellar mass black hole accreting material from a thick disk. The
mechanism for the production of a relativistic wind by such a system is still
unknown. We investigate here one of the proposal where the disk energy is
extracted by a magnetic field amplified to very large values B \sim 10^15 G.
Using some very simple assumptions we compute the mass loss rate along magnetic
field lines and then estimate the Lorentz factor \Gamma at infinity. We find
that \Gamma can reach high values only if severe constraints on the field
geometry and the conditions of energy injection are satisfied. We discuss the
results in the context of different scenarios for GRBs.
