  Accreting black holes (BHs) 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 H-AMR to
study global 3D BH accretion at unusually high resolutions more typical of
local shearing box simulations. We demonstrate that 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 BH 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.
