  Short gamma ray bursts are presumably results of binary neutron star mergers,
which lead to the formation of a stellar mass black hole, surrounded by a
remnant matter. The strong magnetic fields help collimate jets of plasma,
launched along the axis of the black hole rotation. We study the structure and
evolution of the accreting plasma in the short GRBs and we model the formation
of the base of a relativistic, Poynting-dominated jets. Our numerical models
are based on the general relativistic MHD, axisymmetric simulations. We discuss
the origin of variability in the GRB jet emission, which timescales are related
to the action of the magneto-rotational instability in the accreting plasma. We
also estimate the value of a maximum achievable Lorentz factor in the jets
produced by our simulations, and reached at the large distances, where the
gamma ray emission is produced.
