Inclusion Criteria:

          -  Patients between 18 and 65 years old

          -  Patient has a related family member(haploidentical) or unrelated which is 5 of 10 HLA
             identical match.

        Standard Risk

          -  Acute myelogenous leukemia: CR1 with high risk cytogenetics or molecular abnormalities
             such as FLT-3 ITD, or CR2 with a first remission that must have lasted > 1 year.

          -  Acute Lymphocytic Leukemia: CR1, in order to be standard risk must NOT have
             Philadelphia Chromosome.

          -  Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL): Must be refractory
             to fludarabine or fail to have a complete or partial response after therapy with a
             regimen containing fludarabine (or another nucleoside analog, e.g. 2-CDA, pentostatin)
             or experience disease relapse within 12 months after completing therapy with a regimen
             containing fludarabine (or another nucleoside analog).

          -  Chronic myelogenous leukemia: resistant to or intolerant of TKI, in CP1 or CP2, or
             with a mutation that suggests resistance to TKI.

          -  Myelodysplastic Syndrome: RA, RARS, must be IPSS ≥ INT-2, Blasts <5%.

        High Risk Patients:

          -  Acute myelogenous leukemia: Patients with CR2 are considered high risk if they have
             high risk cytogenetics, or molecular abnormalities or CR1 lasted for less than 1 year.
             Any evidence of active disease or no blasts in an acellular marrow.

          -  Acute Lymphocytic Leukemia: CR1- with Ph+ disease, CR2/+ with any cytogenetics. Any
             evidence of active disease.

          -  Chronic myelogenous leukemia- CP2/+, AP1/+, resistant or intolerant to TKI.

          -  Hodgkin's or Non Hodgkin's lymphoma- Disease recurrence following an autologous
             transplant, or high risk disease not thought to benefit from autologous transplant.

          -  Chronic lymphocytic leukemia- that is resistant to fludarabine, and never has been in
             remission or with stable disease/progressive disease

          -  Multiple myeloma: Must have had prior treatment. Patients in CR2 or greater can be
             considered, must have already failed autologous transplant Previous autologous
             transplant,must have been greater than 6 months prior to undergoing this transplant.

          -  Myelodysplastic syndrome: RAEB

          -  Other Myeloproliferative disorders including myelofibrosis, spent phase p
             Vera,Essential thrombocytosis,CMML.

        Exclusion Criteria:

          -  Patients <18 years old Disease related criteria

          -  APML, presence of t(15,17) in first CR

          -  Patients with good risk AML, for example t(8;21), or inv 16, or normal cytogenetics
             with FLT-3-ITD negative, NPM-1 positive disease in 1st CR

          -  MDS IPSS < INT-2 Miscellaneous Criteria

          -  Recipients who have a matched related sibling or unrelated donor

          -  If recipient has evidence of anti-HLA antibodies directed against cord or haplo-donor
             as determined byflowPRA.

        Underlying health criteria:

          -  Zubrod performance status > 2 (see Appendix E)

          -  Life expectancy is limited to less than 8 weeks by concomitant illness

          -  Patients with severely decreased LVEF (EF < 40%)

          -  Impaired pulmonary function tests (PFT's) (FVC, FEV1, DLCO < 45% predicted)

          -  Estimated Creatinine Clearance <50 ml/min

          -  Serum bilirubin> 2.0 mg/dl or SGPT >3 x upper limit of normal

          -  Evidence of chronic active hepatitis or cirrhosis

          -  HIV-positive

          -  Patient is pregnant

          -  Patient or guardian not able to provide informed consent