We propose a simple theoretical formulation of the problem of magnetic
ally driven outflows when poloidal magnetic flux surfaces are absent,
and the magnetic field has only a toroidal component. The present form
ulation is the limiting case of the more general Grad-Shafranov one, w
hen B-p/B-phi --> 0. We show that the toroidal magnetic field alone is
very efficient in accelerating and collimating outflows (jets) from a
ccretion disks. We therefore suggest that the important physical mecha
nism which might be responsible for jet production in the inner part o
f a fully ionized thick accretion disk around an active galactic nucle
us is the buildup of the toroidal magnetic field component by the diff
erential rotation of the disk, and its subsequent escape out of the di
sk. This is qualitatively different from the centrifugal driving mecha
nism of Blandford and Payne (1982), which might be important only in t
he partially ionized parts of the accretion disk where B-p similar to
B-phi. Our formalism is also applied to describe briefly the time-depe
ndent problem.