  We present the results of a series of time-dependent numerical simulations of
cold, magnetocentrifugally launched winds from accretion disks. Our simulations
span four and half decades of mass loading; in the context of a disk with a
launching region from $0.1\AU$ to $1.0\AU$ around a $1\solarmass$ star and a
field strength of about $20\gauss$ at the inner disk edge, this amounts to mass
loss rates of $1\times 10^{-9}$ -- $3\times 10^{-5}\solarmassyear$ from each
side of the disk. We find that the degree of collimation of the wind increases
with mass loading; however even the ``lightest'' wind simulated is
significantly collimated compared with the force-free magnetic configuration of
the same magnetic flux distribution. The implication is that for flows from
young stellar objects a radial field approximation is inappropriate.
Surprisingly, the terminal velocity of the wind and the magnetic lever arm are
still well-described by the analytical solutions for a radial field geometry.
We also find that the isodensity contours and Alfv\'en surface are very nearly
self-similar in mass loading. The wind becomes unsteady above some critical
mass loading rate. For a small enough injection speed, we are able to obtain
the first examples of a class of heavily-loaded magnetocentrifugal winds with
magnetic fields completely dominated by the toroidal component all the way to
the launching surface.
