  We give further considerations on the problem of the evolution of a coronal,
force-free magnetic field which threads a differentially rotating, conducting
Keplerian disk, extending the work of Li {\it et al.} (2001). This situation is
described by the force-free Grad-Shafranov (GS) equation for the flux function
$\Psi(r,z)$ which labels the poloidal field lines (in cylindrical coordinates).
The GS equation involves a function $H(\Psi)$ describing the distribution of
poloidal current which is determined by the differential rotation or {\it
twist} of the disk which increases linearly with time. We numerically solve the
GS equation in a sequence of volumes of increasing size corresponding to the
expansion of the outer perfectly conducting boundaries at ($R_{m}, Z_{m}$). The
outer boundaries model the influence of an external non-magnetized plasma. The
sequence of GS solutions provides a model for the dynamical evolution of the
magnetic field in response to (1) the increasing twist of the disk and (2) the
pressure of external plasma. We find solutions with {\it magnetically
collimated} Poynting jets where there is a {\it continuous} outflow of energy,
angular momentum, and toroidal magnetic flux from the disk into the external
space.
