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, γθ 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.