Sounds like a boost leak to me.
The MAF is detecting the air flow on the inlet side, but, if you have a boost leak then not all the air is getting to the inlet manifold. However the MAF is still going to schedule the fuel as if it is, hence the overfuelling and black smoke. The worse the leak, the more smoke you will get. You may even be able to hear it hiss when the turbo spools up.
Its very common for people to think that the turbo is at fault but in reality that is very unlikely. They do seem to be very robust units.