This study is a research study involving subjects who are diagnosed with a malignant disease, that has either failed standard therapy or is unlikely to be cured with standard non-transplant therapy, who will receive a peripheral blood stem cell transplant. A malignant disease includes the following: Chronic Myeloid Leukemia (CML) in chronic phase, accelerated phase or blast crisis; Acute Myelogenous Leukemia (AML);Myelodysplastic Syndrome (MDS); Juvenile Myelomonocytic Leukemia (JMML); Acute Lymphoblastic Leukemia (ALL); or Lymphoma (Hodgkin's and Non-Hodgkin's) The purpose of this study is to learn more about the effects of CD34+ stem cell selection on graft versus host disease (GVHD) in children, adolescents and young adults. CD34+ stem cells are the cells that make all the types of blood cells in the body. GVHD is a condition that results from a reaction of transplanted donor T-lymphocytes (a kind of white blood cell) against the recipient's body and organs. Study subjects will be offered treatment involving the use of a Miltenyi CliniMacs CD34+ selection device to remove T-cells from a peripheral blood stem cell transplant in order to decrease the risk of acute and chronic GVHD.