This is a pilot study with 2 strata to evaluate engraftment and graft vs. host disease (GVHD) in patients receiving unrelated or partially matched related donor peripheral stem cells using the CliniMACS system to positively deplete T cells to prevent severe GVHD. Feasibility will be tested, focusing on engraftment, treatment-related mortality (with a specific focus on interstitial pneumonitis) and severe GVHD.