Total Body Irradiation/Fludarabine Based Ablative Haploidentical Transplant for Hematologic Diseases

Inclusion Criteria: * No available matched related or unrelated donor OR a matched related or unrelated donor that is unavailable in the time frame necessary * Availability of a 3/6 or 5/6 matched (HLA-A, B, DR) related donor * Donor must have a negative HLA cross-match in the host vs. graft direction * Donor must be willing to donate mobilized peripheral blood stem cells * Age 18 to \</=60 years * Karnofsky Status \>/= 70% * Must have one of the following high-risk malignancies * Chronic Myelogenous Leukemia (CML) in chronic phase, resistant and/or intolerant to TKI * CML in accelerated phase * CML blast crisis that has entered into 2nd Chronic phase following induction * Acute Myelogenous Leukemia (AML) in 2nd or subsequent complete remission (CR) * AML primary induction failure but subsequently in CR * AML in 1st CR with poor risk cytogenetics or arising from preceding hematologic disease * AML with marrow blasts \<5% but persistence of minimal residual disease by flow cytometry, cytogenetics or FISH * Myelodysplastic Syndrome (MDS) that is treatment related * MDS that has monosomy 7 or complex cytogenetics * MDS with IPSS score of 1.5 or greater * Chronic myelomonocytic leukemia (CMML) * Acute Lymphocytic Leukemia/lymphoblastic lymphoma (ALL) in 2nd or subsequent complete remission (CR) * ALL with poor-risk karyotype \[t(9;22) or bcr-abl fusion, t(4;11) or other MLL translocation\] and in 1st CR * ALL with marrow blasts \< 5% but persistence of minimal residual disease by flow cytometry, cytogenetics or FISH * Chronic Lymphocytic Leukemia (CLL)/Prolymphocytic Leukemia (PLL) with previously treated disease that has either relapsed or failed to respond adequately to conventional-dose therapy including purine analogs AND in the opinion of the transplant physician is unlikely to benefit from reduced intensity transplantation due to the presence of one or more high risk features (i.e. bulky tumor masses, B symptoms, and/or inadequate response to salvage chemotherapy) * Hodgkin's or Non-Hodgkin's Lymphoma (including low-grade, mantle cell, and intermediate-grade/diffuse) with previously treated disease that has either relapsed or failed to respond adequately to conventional-dose therapy or autologous transplantation AND in the opinion of the transplant physician is unlikely to benefit from reduced intensity transplantation due to the presence of one or more high risk features (i.e. bulky tumor masses, B symptoms, and/or inadequate response to salvage chemotherapy) * Advance Myelofibrosis, Primary or Post-Polycythemia Vera/Essential Thrombocythemia. Patients must have one of more of the following accelerate phase features, which have been associated with a median overall survival of \</= 15 months * Blood or bone marrow blasts \>/= 10% * Platelets \< 50 x 10\*9/L * Chromosome 17 aberrations Exclusion Criteria: * Patients will not be excluded on the basis of sex, racial or ethnic background * Poor cardiac function: Left ventricular ejection fraction \< 45% * Poor pulmonary function: FEV1 and FVD \< 60% predicted * Poor liver function: bilirubin \>/= 2.5 mg/dl (not due to hemolysis, Gilbert's or primary malignancy), AST/ALT \> 3x ULN * Poor renal function: Creatinine \>/= 2.0 mg/dl or creatinine clearance (calculated creatinine clearance is permitted) \< 40 mL/min based on Traditional Cockcroft-Gault formula: 140-age (yrs) x smaller of actual weight vs ideal body weight (kg)/72 x serum creatinine (mg/dl) * HIV positive * Women of childbearing potential who currently are pregnant or who are not practicing adequate contraception * Patients who have any debilitating medical or psychiatric illness which would preclude their giving informed consent or their receiving optimal treatment and follow-up. * Prior irradiation therapy rendering patient ineligible for TBI