Is there an upper limit to black hole masses?
  We make a case for the existence for ultra-massive black holes (UMBHs) in the Universe, but argue that there exists a likely upper limit to black hole masses of the order of $M \sim 10^{10} \msun$. We show that there are three strong lines of argument that predicate the existence of UMBHs: (i) expected as a natural extension of the observed black hole mass bulge luminosity relation, when extrapolated to the bulge luminosities of bright central galaxies in clusters; (ii) new predictions for the mass function of seed black holes at high redshifts predict that growth via accretion or merger-induced accretion inevitably leads to the existence of rare UMBHs at late times; (iii) the local mass function of black holes computed from the observed X-ray luminosity functions of active galactic nuclei predict the existence of a high mass tail in the black hole mass function at $z = 0$. Consistency between the optical and X-ray census of the local black hole mass function requires an upper limit to black hole masses. This consistent picture also predicts that the slope of the $M_{\rm bh}$-$\sigma$ relation will evolve with redshift at the high mass end. Models of self-regulation that explain the co-evolution of the stellar component and nuclear black holes naturally provide such an upper limit. The combination of multi-wavelength constraints predicts the existence of UMBHs and simultaneously provides an upper limit to their masses. The typical hosts for these local UMBHs are likely the bright, central cluster galaxies in the nearby Universe. 
Priyamvada Natarajan and Ezequiel Treister