  The dynamics and structure of accretion disks, which accumulate the vertical
magnetic field in the centers, are investigated using two- and
three-dimensional MHD simulations. The central field can be built up to the
equipartition level and disrupts a nearly axisymmetric outer accretion disk
inside a magnetospheric radius, forming a magnetically arrested disk (MAD). In
the MAD, the mass accretes in a form of irregular dense spiral streams and the
vertical field, split into separate bundles, penetrates through the disk plane
in low-density magnetic islands. The accreting mass, when spiraling inward,
drags the field and twists it around the axis of rotation, resulting in
collimated Poynting jets in the polar directions. These jets are powered by the
accretion flow with the efficiency up to ~1.5% (in units \dot{M}c^2). The
spiral flow pattern in the MAD is dominated by modes with low azimuthal
wavenumbers m~1-5 and can be a source of quasi-periodic oscillations in the
outgoing radiation. The formation of MAD and Poynting jets can naturally
explain the observed changes of spectral states in Galactic black hole
binaries. Our study is focused on black hole accretion flows; however, the
results can also be applicable to accretion disks around nonrelativistic
objects, such as young stellar objects and stars in binary systems.
