Inclusion Criteria:

          -  Age, Performance Status, and Graft Criteria

               -  Age 0 to 70 years of age with Karnofsky score ≥ 70% (≥ 16 years) or Lansky score
                  ≥ 50 (< 16 years)

               -  Patients ≥ 70 and ≤ 75 years of age may be eligible if they have a HCT-CI
                  Co-Morbidity score ≤ 2

               -  Must be ≥ 3 months after prior myeloablative transplant, if applicable

               -  5/6 or 6/6 related donor match or a 7-8/8 HLA-A,B,C,DRB1 allele matched unrelated
                  donor marrow and/or PBSC donor match per current institutional guidelines Related
                  donors will be evaluated and collected per MT2012-14C; Unrelated donors will be
                  identified and collected per usual procedures

          -  Eligible Diseases

               -  Acute Myeloid Leukemia (AML): high risk CR1 (as evidenced by preceding MDS, high
                  risk cytogenetics, ≥ 2 cycles to obtain CR, erythroblastic or megakaryocytic
                  leukemia, FLT-3 ITD +; CR2+. All patients must be in CR as defined by
                  hematological recovery, AND <5% blasts by light microscopy within the bone marrow
                  with a cellularity of ≥15%.

               -  Very high risk pediatric patients with AML: Patients <21 years, however, are
                  eligible with (M2 marrow) with < 25% blasts in marrow after having failed one or
                  more cycles of chemotherapy.

               -  Acute Lymphocytic Leukemia (ALL): factor that define high risk CR1 include but
                  are not limited to cytogenetics demonstrating t(9;22), t (1:19), t(4;11), other
                  MLL rearrangements, hypodiploidy, or IKZF1 abnormalities), DNA index < 0.81, > 1
                  cycle to obtain CR or presence minimal residual disease (MRD). Patients in CR2+
                  are eligible. All patients must be in CR as defined by hematological recovery,
                  AND <5% blasts by light microscopy within the bone marrow with a cellularity of
                  ≥15%.

               -  Very high risk pediatric patients with ALL: patients <21 years are also
                  considered high risk CR1 if they had M2 or M3 marrow at day 42 from the
                  initiation of induction or M3 marrow at the end of induction. They are eligible
                  once they achieved a complete remission.

               -  Chronic Myelogenous Leukemia excluding refractory blast crisis: To be eligible in
                  first chronic phase (CP1) patient must have failed or be intolerant to imatinib
                  mesylate.

               -  Plasma Cell Leukemia after initial therapy, who achieved at least a partial
                  remission

               -  Myelodysplasia (MDS) requiring transplant as defined as: IPSS INT-2 or High Risk;
                  R-IPSS High or Very High; WHO classification: RAEB-1, RAEB-2; Severe Cytopenias:
                  ANC < 0.8, Anemia or thrombocytopenia requiring transfusion; Poor or very poor
                  risk cytogenetics based on IPSS or R-IPSS definitions; therapy-related MDS.
                  Blasts must be < 5% by bone marrow aspirate morphology.

               -  Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma (CLL/SLL), Marginal Zone
                  B-Cell Lymphoma or Follicular Lymphoma are eligible if there was disease
                  progression/relapse within 12 of achieving a partial or complete remission.
                  Patients who had remissions lasting > 12 months, are eligible after at least two
                  prior therapies. Patients with bulky disease (nodal mass greater than 5 cm)
                  should be considered for de-bulking chemotherapy before transplant.

               -  Lymphoplasmacytic Lymphoma, Mantle-Cell Lymphoma, Prolymphocytic Leukemia, NK
                  cell malignancies are eligible after initial therapy in CR1+ or PR1+.

               -  Large Cell NHL > CR2/> PR2: Patients in CR2/PR2 with initial short remission (<6
                  months) are eligible.

               -  Lymphoblastic Lymphoma, Burkitt's Lymphoma, and other high-grade NHL after
                  initial therapy if stage III/IV in CR1/PR1 or after progression if stage I/II < 1
                  year.

               -  Multiple Myeloma beyond PR2: Patients with chromosome 13 abnormalities, first
                  response lasting less than 6 months, or β-2 microglobulin > 3 mg/L, may be
                  considered for this protocol after initial therapy.

               -  Myeloproliferative Syndromes

          -  Organ Function Criteria Adequate organ function is defined as:

               -  Liver: AST and ALT < 5 x upper limit of normal and bilirubin < 3 x upper limit of
                  normal

               -  Renal: Creatinine ≤ 2.0 mg/dl (adults) and estimated glomerular filtration rate
                  (GFR) ≥ 40 mL/min (pediatrics). Adults with a creatinine > 1.2 mg/dl or a history
                  of renal dysfunction must have estimated glomerular filtration rate (GFR) > 40
                  mL/min.

               -  Albumin > 2.5 g/dL

               -  Cardiac: Absence of decompensated congestive heart failure, or uncontrolled
                  arrhythmia and left ventricular ejection fraction > 35%.

               -  Pulmonary: DLCOcorr ≥ 40% predicted, and absence of O2 requirements. For children
                  that are not able to cooperate with PFTs, a pulse oximetry with or without
                  exercise should be attempted. If neither test can be obtained it should be
                  clearly stated in the physician's note.

          -  If recent mold infection (e.g. aspergillus) must have minimum of 30 days of therapy
             and responsive disease and be cleared by Infectious Disease

          -  Females of child bearing potential and sexually active males must agree to use
             adequate birth control during study treatment

          -  Voluntary written consent (adult or parent/guardian with presentation of the minor
             information sheet, if appropriate)

        Exclusion Criteria:

          -  Pregnant or breast feeding. The agents used in this study include Pregnancy Category
             D: known to cause harm to a fetus. Females of childbearing potential must have a blood
             test or urine study within 14 days prior to registration to rule out pregnancy.

          -  Untreated active infection

          -  Active CNS disease

          -  Active HIV infection or known HIV positive serology

          -  Congenital bone marrow failure syndrome

          -  Previous irradiation that precludes the safe administration of an additional dose of
             200 cGy of TBI

          -  CML in refractory blast crisis

          -  Intermediate or high grade NHL, mantle cell NHL, and Hodgkin disease that is
             progressive on salvage therapy. Stable disease is acceptable to move forward provided
             it is non-bulky.

          -  Multiple myeloma progressive on salvage chemotherapy