  Accreting black holes produce collimated outflows, or jets, that traverse
many orders of magnitude in distance, accelerate to relativistic velocities,
and collimate into tight opening angles. Of these, perhaps the least understood
is jet collimation due to the interaction with the ambient medium. In order to
investigate this interaction, we carried out axisymmetric general relativistic
magnetohydrodynamic simulations of jets produced by a large accretion disc,
spanning over 5 orders of magnitude in time and distance, at an unprecedented
resolution. Supported by such a disc, the jet attains a parabolic shape,
similar to the M87 galaxy jet, and the product of the Lorentz factor and the
jet half-opening angle, $\gamma\theta\ll 1$, similar to values found from very
long baseline interferometry (VLBI) observations of active galactic nuclei
(AGN) jets; this suggests extended discs in AGN. We find that the interaction
between the jet and the ambient medium leads to the development of pinch
instabilities, which produce significant radial and lateral variability across
the jet by converting magnetic and kinetic energy into heat. Thus pinched
regions in the jet can be detectable as radiating hotspots and may provide an
ideal site for particle acceleration. Pinching also causes gas from the ambient
medium to become squeezed between magnetic field lines in the jet, leading to
enhanced mass-loading of the jet and potentially contributing to the
spine-sheath structure observed in AGN outflows.
