Inclusion Criteria:

* Age 0 to 75 years of age with Karnofsky score ≥ 70% (≥ 16 years) or Lansky score ≥ 50 (\< 16 years).
* 5/6 or 6/6 related donor, OR a 7-8/8 HLA-A, B, C, DRB1 allele match, OR a haplotype (at least 5/10) matched related donor. Donors will be requested to provide PBSCs although bone marrow is acceptable according to donor preference.

Eligible Diseases Acute Leukemias: Must be in remission by morphology (≤5% blasts) AND without evidence of MRD by flow cytometry, FISH, or conventional cytogenetics. PCR based MRD detection is not an exclusion to proceed.

Acute Myeloid Leukemia (AML) and related precursor neoplasms:

2nd or greater complete remission (CR); first complete remission (CR1) in patients \> 60 years old; CR1 in ≤ 60 years old that is NOT considered as favorable-risk.

Favorable risk AML is defined as having one of the following:

* t(8,21) without cKIT mutation
* inv(16) or t(16;16) without cKIT mutation
* Normal karyotype with mutated NPM1 and wild type FLT-ITD (unless persistently NPM1 positive by PCR following two cycles of chemotherapy)
* Normal karyotype with double mutated CEBPA
* Acute prolymphocytic leukemia (APL) in first molecular remission at the end of consolidation

Acute lymphoblastic Leukemia (ALL) /lymphoma:

CR2 or greater, CR1 unable to tolerate consolidation chemotherapy due to chemotherapy-related toxicities; CR1 high-risk ALL.

High risk ALL is defined as having one of the following:

* Evidence of high risk cytogenetics, e.g. t(9;22), t(1;19), t(4;11), other MLL rearrangements, IKZF1
* 30 years of age or older at diagnosis
* White blood cell counts of greater than 30,000/mcL (B-ALL) or greater than 100,000/mcL (T-ALL) at diagnosis
* CNS leukemia involvement during the course of disease
* Slow cytologic response (\>10% lymphoblasts in bone marrow on Day 14 of induction therapy)
* Evidence of persistent immonophenotypic or molecular minimal residual disease (MRD) at the end of induction and consolidation therapy.

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.

Biphenotypic/Undifferentiated/Prolymphocytic Leukemias in first or subsequent CR.

Chronic Myelogenous Leukemia in chronic or accelerated phase, or CML blast crisis in morphological remission (\<5% blasts) and with negative MRD by flow cytometry (a positive PCR for BCRABL is acceptable for BMT): Chronic phase patients must have failed at least two different TKIs, been intolerant to all available TKIs or have T315I mutation. Patients with CML blast crisis in CR are only eligible if there is an feasible TKI maintenance plan following BMT.

Plasma Cell Leukemia after initial therapy, who achieved at least a partial remission; or relapsed and achieved subsequent remission (CR/PR) Myelodysplastic Syndrome: 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. If ≥5% blasts, patient requires chemotherapy for cytoreduction to \<5% blasts prior to transplantation Leukemia or MDS in aplasia. These patients may be taken to transplant if after induction therapy they remain with aplastic bone marrow and no morphological or flow-cytometry evidence of disease ≥ 28 days post-therapy. These high risk patients will be analyzed separately.

Burkitt's Lymphoma in CR2 or subsequent CR. Relapsed T-Cell Lymphoma that is chemotherapy sensitive in CR/PR that has failed or ineligible for an autologous transplantNatural Killer Cell Malignancies. Relapsed Chronic Lymphocytic Leukemia/Small Lymphocytic Lymphoma (CLL/SLL), Marginal Zone B-Cell Lymphoma or Follicular Lymphoma which have progressed within 12 months 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 should be considered for de-bulking chemotherapy before transplant. Patients with refractory disease may be eligible, unless bulky disease and an estimated tumor doubling time of less than one month.

Lymphoplasmacytic Lymphoma, Mantle-Cell Lymphomais eligible after initial therapy if chemotherapy sensitive.

Large Cell and other high risk NHL \> CR2/\> PR2: Patients in CR2/PR2 with initial short remission (\<6 months) are eligible.

Relapsed Multiple Myeloma: that is chemotherapy sensitive and has failed or ineligible for an autologous transplant.

Myeloproliferative Neoplasms/Myelofibrosis - with transfusion dependence or expected survival under 5 years by DIPSS, DIPSS-plus, or MPSS70 calculator.

Acquired Bone Marrow Failure Syndromes except for Fanconi anemia Other Leukemia Subtypes: A major effort in the field of hematology is to identify patients who are of high risk for treatment failure so that patients can be appropriately stratified to either more (or less) intensive therapy. This effort is continually ongoing and retrospective studies identify new disease features or characteristics that are associated with treatment outcomes. Therefore, if new features are identified after the writing of this protocol, patients can be enrolled with the approval of two members of the study committee.

Additional Criteria for Bulky Disease (lymphomas) if stable disease is best response, the largest residual nodal mass must \< 5 cm (approximately) If response to previous therapy, the largest residual mass must represent a 50% reduction and be \< 7.5 cm (approximately)

Organ Function Criteria

Adequate organ function is defined as:

Liver: Transaminases ≤ 5 x upper limit of normal (ULN) and total bilirubin ≤ 2.5 mg/dL except for patients with Gilbert's syndrome or hemolysis.

Renal: A normal creatinine (adults) or creatinine clearance ≥ 40 mL/min (pediatrics). Adults with a creatinine \> 1.2 mg/dl or a history of renal dysfunction must have estimated GFR ≥ 40 ml/min/1.73m2.

Cardiac: Absence of decompensated congestive heart failure, or uncontrolled arrhythmia and left ventricular ejection fraction \> 40%. For children that are not able to cooperate with MUGA and echocardiography, such should be clearly stated in the physician's note.

Pulmonary: DLCO, FEV1, FVC ≥ 40% predicted, and absence of O2 requirements. For children that are not able to cooperate with PFTs, a pulse oximetry with exercise should be attempted. If neither test can be obtained it should be clearly stated in the physician's note.

If recent confirmed mold infection (e.g. aspergillus) must have minimum of 30 days of therapy and responsive disease and be cleared by Infectious Disease HIV infection with undetectable viral load. All HIV+ patients must be evaluated by Infectious Disease (ID) and a HIV management plan establish prior to transplantation Sexually active females of child bearing potential and sexually active males with partners of child bearing potential 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)

Related donors will be evaluated and collected according to UMN BMT program standard processes. Unrelated donors will be identified and collected through the National Marrow and Donor Program (NMDP) per usual steps.

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 negative pregnancy test prior to starting therapy.
* Untreated active infection
* Active central nervous system malignancy
* CML in 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.
* Less than 3 months since prior myeloablative transplant
* Evidence of progressive disease by imaging modalities or biopsy - persistent PET activity, though possibly related to lymphoma, is not an exclusion criterion in the absence of CT changes indicating progression.