RecruitingBiological interventionStem Cell Transplant From Donors After Alpha Beta Cell Depletion in Children and Young AdultsThe purpose of the CliniMACS® TCRαβ-Biotin System and CliniMACS® CD19 is to improve the safety and efficacy of allogeneic HLA-partially matched related or unrelated donors HSCT when no matched donors are available, to treat malignant and nonmalignant disorders for which HSCT is the recommended best available therapy. Initially this device will be used in a single-center, open-label, single-arm, phase II clinical trial to evaluate the efficacy of haploidentical PBSC grafts depleted of TCRα/β+ and CD19+ cells using the CliniMACS® TCRαβ/CD19 System in children and adults with hematological and non-hematological malignancies.