We present self-consistent solutions of the full set of ideal MHD equa
tions which describe steady-state relativistic cold outflows from thin
accretion disks. The magnetic field forms a spiral which is anchored
in the disk, rotates with it, and accelerates the how out of the disk
plane. The collimation at large distances depends on the total amount
of electric current that flows along the jet. We considered various di
stributions of electric current and derived the result that in straigh
t jets which extend to infinite distances, a strong electric current f
lows along their axis of symmetry. The asymptotic flow velocities are
of the order of the initial rotational velocity at the base of the how
(a few tenths of the speed of light). The solutions are applied to bo
th galactic (small-scale) and extragalactic (large-scale) jets.