  Prevalent around luminous accreting black holes, thin discs are challenging
to resolve in numerical simulations. When the disc and black hole angular
momentum vectors are misaligned, the challenge becomes extreme, requiring
adaptive meshes to follow the disc proper as it moves through the computational
grid. With our new high-performance general relativistic magnetohydrodynamic
(GRMHD) code H-AMR we have simulated the thinnest accretion disc to date, of
aspect ratio H/R~0.03, around a rapidly spinning (a=0.9375) black hole, using a
cooling function. Initially tilted at 10 degrees, the disc warps inside r~5 r_g
into alignment with the black hole, where r_g is the gravitational radius. This
is the first demonstration of Bardeen-Petterson alignment in MHD with viscosity
self-consistently generated by magnetized turbulence. The disc develops a
low-density high-viscosity (alpha_eff ~ 1.0) magnetic-pressure--dominated inner
region at r<25 r_g that rapidly empties itself into the black hole. This inner
region may in reality, due to thermal decoupling of ions and electrons,
evaporate into a radiatively inefficient accretion flow if, as we propose, the
cooling time exceeds the accretion time set by the order unity effective
viscosity. We furthermore find the unexpected result that even our very thin
disc can sustain large-scale vertical magnetic flux on the black hole, which
launches powerful relativistic jets that carry 20-50% of the accretion power
along the angular momentum vector of the outer tilted disc, providing a
potential explanation for the origin of jets in radio-loud quasars.
