Oh . . .I don't know! This probably doesn't answer your question but it's all I could find . . .sounds like it's what's left in the mom?:
If one chooses to donate their baby's cord blood, the following process will take place. After the doctor or nurse determine that the mother and baby are in good condition and the cord has been cut and clamped, the leftover cord blood will be collected from the mother's side. The cord and placenta are drained and the tissue will be discarded according to the hospital routine. The collection is done by your doctor or nurse, after they determine that you and your baby are in good condition.
from
http://www.lifesource.org/who_cord.asp