We present a class of self-similar solutions which represent force-fre
e, axisymmetric, special relativistic, ideal, magnetohydrodynamic, col
limated outflows (jets) from magnetized accretion disks around compact
objects. The solutions extend to large distances beyond the light cyl
inder, and capture many of the important processes of how acceleration
present in more general non-force-free solutions. We show that the im
portant factor which determines the general morphology (degree of coll
imation) and the asymptotic Lorentz factor of the outflow is the distr
ibution and total amount of electric current which hows along the jet.
The present work makes the connection between the works of Li, Chiueh
, & Begelman (1992) and Contopoulos (1994).