Stars protuberances What happens with stars protuberances (irregularities in the shape of the stars) when they collapse to form a black hole?
I have read that according to the classical theory, the bulges are radiared away. But what happens with those bulges when we factor quantum effects in(semiclassical rheory)?
 A: At those energy levels, before they have collapsed, the energy levels do not need quantum gravity to describe what happens gravitationally. You might need a quantum description of matter, but classical General Relativity will still hold. In most cases just a perfect or imperfect fluid model, with perturbations if you need them, works well. 
The exceptions might be during critical collapse after shrinking due to Hawking radiation, then semi classical results can be different. See  http://relativity.livingreviews.org/open?pubNo=lrr-1999-4&page=node25.html. The quantum gravity and field theory is reviewed nicely in https://arxiv.org/pdf/1409.1231.pdf. 
So, yes, General Relativity theorems (No Hair Theorem) and calculations of collapse scenarios (linked the first one, pure dust, then others, and in quite a few cases also perturbation calculations representing the protuberances) is that they radiate away, as gravitational radiation, or in more dynamic interactive matter collapse some of the matter gets kicked off. But as collapse nears completion the perturbations from the end states get radiated away as gravitational radiation (maybe mostly). One result is that anything that could radiate away does - only the conserved quantities that define the leftover 'hair' of the Black Hole remains. Thus, dipole moment does not radiate in General Relativiy, nor monopole moment, and so mass and spin are two remaining 'hair'. Charge is the third. Quadrupole and higher moments get radiated away. As I said above this has been confirmed with perturbations calculations/simulations, and is required by the theory on the possible end results being only the spherically symmetric Schwarzschild and Kerr (and it's charged versions) Black Holes. At least for non quantum gravity.
See also the related question and answers at How Smooth is an Event Horizon?
