  Astrophysical disks are likely embedded in an ambient vertical magnetic
field. This ambient field is known to drive magneto-rotational turbulence in
the disk bulk but is also responsible for the launching of magnetized outflows
at the origin of astrophysical jets. The vertical structure and long-term
(secular) evolution of such a system lack quantitative predictions. It is
nevertheless this secular evolution that is proposed to explain time
variability in many accreting systems such as X-ray binaries. We compute and
analyze global 3D ideal-MHD simulations of an accretion disk threaded by a
large-scale magnetic field. We evaluate the role of the turbulent terms in the
equilibrium of the system. We then compute the transport of mass, angular
momentum, and magnetic fields in the disk to characterize its secular
evolution. We perform a parameter survey to characterize the influence of disk
properties on secular transport.
  We find that weakly magnetized disks drive jets that carry away a small
fraction of the disk angular momentum. The mass-weighted accretion speed
remains subsonic although, there is always an upper turbulent atmospheric
region where transonic accretion takes place. We show that a strongly
magnetized version of the magneto-rotational instability drives this
turbulence. The disk structure is drastically different from the conventional
hydrostatic picture. The magnetic field is always dragged inwards in the disk,
at a velocity that increases with the disk magnetization. Beyond a threshold on
the latter, the disk undergoes a profound radial readjustment. It leads to the
formation of an inner accretion-ejection region with a supersonic mass-weighted
accretion speed and where the magnetic field distribution becomes steady, near
equipartition with the thermal pressure. This inner structure shares many
properties with the Jet Emitting Disk model described by Ferreira (1997).
