  We investigate the physical properties of equilibrium sequences of
non-self-gravitating surfaces that characterize thick disks around a rotating
deformed compact object described by a stationary generalization of the static
q-metric. The spacetime corresponds to an exact solution of Einstein's field
equations so that we can perform the analysis for arbitrary values of the
quadrupole moment and rotation parameter. To study the properties of this
disk's model, we analyze bounded trajectories in this spacetime. Further, we
find that depending on the values of the parameters, we can have various disc
structures that can easily be distinguished from the static case and also from
the Schwarzschild background. We argue that this study may be used to evaluate
the rotation and quadrupole parameters of the central compact object.
