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 _ { * } | \leq 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 .