Accreting black holes launch relativistic collimated jets, across many decades in luminosity and mass, suggesting the jet launching mechanism is universal, robust and scale-free. Theoretical models and general relativistic magnetohydrodynamic (GRMHD) simulations indicate that the key jet-making ingredient is large-scale poloidal magnetic flux. However, its origin is uncertain, and it is unknown if it can be generated in situ or dragged inward from the ambient medium. Here, we use the GPU-accelerated GRMHD code HAMR to study global 3D black hole accretion at unusually high resolutions more typical of local shearing box simulations. We demonstrate that accretion disc turbulence in a radially-extended accretion disc can generate large-scale poloidal magnetic flux in situ, even when starting from a purely toroidal magnetic field. The flux accumulates around the black hole till it becomes dynamically-important, leads to a magnetically arrested disc (MAD), and launches relativistic jets that are more powerful than the accretion flow. The jet power exceeds that of previous GRMHD toroidal field simulations by a factor of 10,000. The jets do not show significant kink or pinch instabilities, accelerate to $gamma sim 10$ over 3 decades in distance, and follow a collimation profile similar to the observed M87 jet.
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