In this Letter we revisit arguments suggesting that the Bardeen-Petterson effect can coalign the spins of a central supermassive black hole binary accreting from a circumbinary (or circumnuclear) gas disc. We improve on previous estimates by adding t
he dependence on system parameters, and noting that the nonlinear nature of warp propagation in a thin viscous disc affects alignment. This reduces the discs ability to communicate the warp, and can severely reduce the effectiveness of disc-assisted spin alignment. We test our predictions with a Monte Carlo realization of random misalignments and accretion rates and we find that the outcome depends strongly on the spin magnitude. We estimate a generous upper limit to the probability of alignment by making assumptions which favour it throughout. Even with these assumptions, about 40% of black holes with $a gtrsim 0.5$ do not have time to align with the disc. If the residual misalignment is not small and it is maintained down to the final coalescence phase this can give a powerful recoil velocity to the merged hole. Highly spinning black holes are thus more likely of being subject to strong recoils, the occurrence of which is currently debated.
Recent observations point to the presence of structured dust grains in the discs surrounding young brown dwarfs, thus implying that the first stages of planet formation take place also in the sub-stellar regime. Here, we investigate the potential for
planet formation around brown dwarfs and very low mass stars according to the sequential core accretion model of planet formation. We find that, for a brown dwarfs of mass 0.05M_{odot}, our models predict a maximum planetary mass of ~5M_{oplus}, orbiting with semi-major axis ~1AU. However, we note that the predictions for the mass - semi-major axis distribution are strongly dependent upon the models chosen for the disc surface density profiles and the assumed distribution of disc masses. In particular, if brown dwarf disc masses are of the order of a few Jupiter masses, Earth-mass planets might be relatively frequent, while if typical disc masses are only a fraction of Jupiter mass, we predict that planet formation would be extremely rare in the sub-stellar regime. As the observational constraints on disc profiles, mass dependencies and their distributions are poor in the brown dwarf regime, we advise caution in validating theoretical models only on stars similar to the Sun and emphasise the need for observational data on planetary systems around a wide range of stellar masses. We also find that, unlike the situation around solar-like stars, Type-II migration is totally absent from the planet formation process around brown dwarfs, suggesting that any future observations of planets around brown dwarfs would provide a direct measure of the role of other types of migration.
