Mole Removal Question - Need Help!

Hi folks,
I have a question. I just had two moles removed today from a dermatologist at my local hospital. He first cauterized the moles and then used a tweezer to pick out the burnt skin apart and then had the wounds cauterized again to stop the bleeding. I've just changed the plaster on my wounds now and noticed that the dermatologist did not fully remove the moles. He's removed around 2 quarters of one mole and there's still some black bits of the mole remaining. I was just wondering if this was normal? Would the remaining burnt mole bits just fall off when new skin grows? or is this something to worry about?

[mudder147]

are you sure the black bits are not from having it  cauterized ?