  In this paper we extend our previous works on spherically symmetric accretion
onto black holes and super-spinars to the case in which the fluid has a finite
angular momentum initially. We run 2.5D and 3D general relativistic
hydrodynamic simulations of the accretion of a fat disk. We study how the
accretion process changes by changing the values of the parameters of our
model. We show that the value of the fluid angular momentum critically
determines turn-on and off the production of powerful equatorial outflows
around super-spinars. For corotating disks, equatorial outflows are efficiently
generated, even for relatively low spin parameters or relatively large
super-spinar radii. For counterrotating disks, equatorial outflows are instead
significantly suppressed, and they are possible only in limited cases. We also
study accretion around a tilted disk.
