  When a black hole is accreting well below the Eddington rate, a geometrically
thick, radiatively inefficient state of the accretion disk is established.
There is a limited number of closed-form physical solutions for geometrically
thick (non-selfgravitating) toroidal equilibria of perfect fluids orbiting a
spinning black hole, and these are predominantly used as initial conditions for
simulations of accretion in the aforementioned mode. However, different initial
configurations might lead to different results and thus observational
predictions drawn from such simulations.
  We expand the known equilibria by a number of closed multiparametric
solutions with various possibilities of rotation curves and geometric shapes.
Then, we ask whether choosing these as initial conditions influences the onset
of accretion and the asymptotic state of the disk.
  We investigate a set of examples from the derived solutions in detail; we
analytically estimate the growth of the magneto-rotational instability (MRI)
from their rotation curves and evolve the analytically obtained tori using the
2D magneto-hydrodynamical code HARM. Properties of the evolutions are then
studied through the mass, energy, and angular-momentum accretion rates.
  The rotation curve has a decisive role in the numerical onset of accretion in
accordance with our analytical MRI estimates: In the first few orbital periods,
the average accretion rate is linearly proportional to the initial MRI rate in
the toroids. The final state obtained from any initial condition within the
studied class after an evolution of $\gtrsim 10$ orbital periods is mostly
qualitatively identical and the quantitative properties vary within a single
order of magnitude. The average values of the energy of the accreted fluid have
an irregular dependency on initial data, and in some cases fluid with energies
many times its rest mass is systematically accreted.
