We present the first general relativistic hydrodynamic models of the launch and evolution of relativistic jets and winds, driven by thermal energy deposition, possibly due to neutrino-antineutrino annihilation, in the close vicinity of black hole-accretion torus systems. The latter are considered to be the remnants of compact object mergers. Our two-dimensional simulations establish the link between models of such mergers and future observations of short gamma-ray bursts by the SWIFT satellite. They show that ultrarelativistic outflow with maximum terminal Lorentz factors around 1000 develops for polar energy deposition rates above some 10(48) erg s(-1) per steradian, provided the merger environment has a sufficiently low baryon density. By the interaction with the dense accretion torus the ultrarelativistic outflow with Lorentz factors Gamma above 100 is collimated into a sharp-edged cone that is embedded laterally by a wind with steeply declining Lorentz factor. The typical semi-opening angles of the Gamma > 100 cone are 5 degrees-10 degrees, corresponding to about 0.4-1.5% of the hemisphere and apparent isotropized energies (kinetic plus internal) up to approximate to 10(51) erg although at most 10-30% of the deposited energy is transferred to the outflow with Gamma > 100. The viability of post-merger black hole-torus systems as engines of short, hard gamma-ray bursts is therefore confirmed. The annihilation of neutrino-antineutrino pairs radiated from the hot accretion torus appears as a suitable energy source for powerful axial outflow even if only approximate to 10(49) erg are deposited within a cone of 45 degrees half-opening angle around the system axis. Although the torus lifetimes are expected to be only between some 0.01 s and several 0.1 s, our models can explain the durations of all observed short gamma-ray bursts, because different propagation velocities of the front and rear ends will lead to a radial stretching of the ultrarelativistic fireball before transparency is reached. The ultrarelativistic flow reveals a highly non-uniform structure caused by the action of Kelvin-Helmholtz instabilities that originate at the fireball-torus interface. Large radial variations of the baryon density (up to several orders of magnitude) are uncorrelated with moderate variations of the Lorentz factor (factors of a few) and fluctuations of the gently declining radiation-dominated pressure. In the angular direction the Lorentz factor reveals a nearly flat plateau-like maximum with values of several hundreds, that can be located up to 7 degrees off the symmetry axis, and a steep decrease to less than 10 for polar angles larger than 15 degrees-20 degrees. Lateral expansion of the ultrarelativistic core of the flow is prevented by a subsonic velocity component of about 0.05c towards the symmetry axis, whereas the moderately relativistic wings show a subsonic sideways inflation with less than 0.07c (measured in the frame comoving with the radial flow).
