  We present self-consistent global, steady-state MHD models and synthetic
optically thin synchrotron emission maps for the jet of M87. The model consist
of two distinct zones: an inner relativistic outflow, which we identify with
the observed jet, and an outer cold disk-wind. While the former does not
self-collimate efficiently due to its high effective inertia, the latter
fulfills all the conditions for efficient collimation by the
magneto-centrifugal mechanism. Given the right balance between the effective
inertia of the inner flow and the collimation efficiency of the outer disk
wind, the relativistic flow is magnetically confined into a well collimated
beam and matches the measurements of the opening angle of M87 over several
orders of magnitude in spatial extent. The synthetic synchrotron maps reproduce
the morphological structure of the jet of M87, i.e. center-bright profiles near
the core and limb-bright profiles away from the core. At the same time, they
also show a local increase of brightness at some distance along the axis
associated to a recollimation shock in the MHD model. Its location coincides
with the position of the optical knot HST-1. In addition our best fitting model
is consistent with a number of observational constraints such as the magnetic
field in the knot HST-1, and the jet-to-counterjet brightness ratio.
