Luminous active galactic nuclei (AGN) and X-Ray binaries (XRBs) tend to be surrounded by geometrically thin, radiatively cooled accretion discs. According to both theory and observations, these are -- in many cases -- highly misaligned with the black hole spin axis. In this work we present the first general relativistic magnetohydrodynamic simulations of very thin ($h/r sim 0.015-0.05$) accretion discs around rapidly spinning ($a sim 0.9$) black holes and tilted by 45-65 degrees. We show that the inner regions of the discs with $h/r lesssim 0.03$ align with the black hole equator, though at smaller radii than predicted by theoretical work. The inner aligned and outer misaligned disc regions are separated by a sharp break in tilt angle accompanied by a sharp drop in density. We find that frame-dragging by the spinning black hole overpowers the disc viscosity, which is self-consistently produced by magnetized turbulence, tearing the disc apart and forming a rapidly precessing inner sub-disc surrounded by a slowly precessing outer sub-disc. We find that at all tilt values the system produces a pair of relativistic jets. At small distances the jets precess rapidly together with the inner sub-disc, whereas at large distances they partially align with the outer sub-disc and precess more slowly. If the tearing radius can be modeled accurately in future work, emission model independent measurements of black hole spin based on precession-driven quasi-periodic oscillations may become possible.
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