  Unconfined relativistic outflows from rotating, magnetized compact objects
are often well-modeled by assuming the field geometry is approximately a
split-monopole at large radii. Earlier work has indicated that such an
unconfined flow has an inefficient conversion of magnetic energy to kinetic
energy. This has led to the conclusion that ideal magnetohydrodynamical (MHD)
processes fail to explain observations of, e.g., the Crab pulsar wind at large
radii where energy conversion appears efficient. In addition, as a model for
astrophysical jets, the monopole field geometry has been abandoned in favor of
externally confined jets since the latter appeared to be generically more
efficient jet accelerators. We perform time-dependent axisymmetric relativistic
MHD simulations in order to find steady state solutions for a wind from a
compact object endowed with a monopole field geometry. Our simulations follow
the outflow for 10 orders of magnitude in distance from the compact object,
which is large enough to study both the initial "acceleration zone" of the
magnetized wind as well as the asymptotic "coasting zone." We obtain the
surprising result that acceleration is actually {\it efficient} in the polar
region, which develops a jet despite not being confined by an external medium.
Our models contain jets that have sufficient energy to account for moderately
energetic long and short gamma-ray burst (GRB) events (~10^{51}--10^{52} erg),
collimate into narrow opening angles (opening half-angle \theta_j \approx 0.03
rad), become matter-dominated at large radii (electromagnetic energy flux per
unit matter energy flux \sigma<1), and move at ultrarelativistic Lorentz
factors (\gamma_j ~ 200 for our fiducial model). (abridged)
