  There is robust observational evidence supporting the existence of $5 - 20$
$M_\odot$ compact bodies in X-ray binary systems and of $10^5 - 10^9$ $M_\odot$
bodies at the center of many galaxies. All these objects are commonly
interpreted as black holes, even is there is no direct evidence that they have
an event horizon. A fundamental limit for a black hole in 4-dimensional general
relativity is the Kerr bound $|a_*| \le 1$, where $a_*$ is the spin parameter.
This is just the condition for the existence of the event horizon. The
accretion process can spin a black hole up to $a_* \approx 0.998$ and some
super-massive objects in galactic nuclei could be rapidly rotating black holes
with spin parameter close to this limit. However, if these super-massive
objects are not black holes, the Kerr bound does not hold and the accretion
process can spin them up to $a_* > 1$. In this paper, I consider compact bodies
with non-Kerr quadrupole moment. I study the evolution of the spin parameter
due to accretion and I find its equilibrium value. Future experiments like the
gravitational wave detector LISA will be able to test if the super-massive
objects at the center of galaxies are the black holes predicted by general
relativity. If they are not black holes, some of them may be super-spinning
objects with $a_* > 1$.
