The purpose of this research study is to test a new method of cell processing for stem cell transplants with an unrelated donor or partially matched related donor for patients with BMF who do not have a well matched related donor. The new method is called alpha/beta T cell and B cell depletion using a device called CliniMACs.  We want to see if this method can reduce some of the complications of the transplant and decrease the time it takes for the new stem cells to establish a new immune system.