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 .