Inclusion Criteria:

1. Patients < 55 years (Myeloablative regimen 1) or >/ = 55 and intensity regimen 2) old lacking a matched related volunteer donor identified in time
for transplant for which a related haploidentical donor ( A, B, C, DR loci), a 7/8 allele matched related or unrelated donor is identified, or
a matched unrelated donor (MUD) .

2. Acute lymphocytic leukemia (ALL) in CR1 with high-risk features including adverse
cytogenetics such as t(9;22), t(1;19), t(4;11), or MLL gene rearrangements; ALL in
second or greater remission or ALL with relapsed disease, peripheral blood blasts <
1000/microliter, ALL patients must show response to most recent received
chemotherapy;

3. Acute myeloid leukemia (AML) in CR1 with intermediate-risk disease or high-risk
features defined as: Greater than 1 cycle of induction therapy required to achieve
remission; Preceding myelodysplastic syndrome (MDS) or myeloproliferative disease;
Presence of FLT3 mutations or internal tandem duplications; FAB M6 or M7
classification; Adverse cytogenetics, -5, del 5q, -7, del7q, abnormalities involving
3q, 9q, 11q, 20q, 21q, 17, +8 [> 3 abnormalities], peripheral blood blasts
<1000/microliter, AML patients must show response to most recent received
chemotherapy;

4. AML in second or greater remission, primary induction failure and patients with
relapsed disease, peripheral blood blasts <1000/microliter;

5. Myelodysplastic syndrome (MDS) with International Prognostic Scoring System (IPSS)
intermediate-2 or higher; or therapy-related MDS

6. Aplastic anemia with Absolute neutrophil count (ANC)<1000 and transfusion dependent
after they failed immunosuppression therapy

7. Chronic myeloid leukemia (CML) >/=1st chronic phase, after failed >/=2 lines of
tyrosine kinase inhibitors; in accelerated or blast phase with > 30% bone marrow
blasts;

8. Prior allogeneic stem cell transplant more than 6 months from the first transplant,
in remission.

9. Chemotherapy-sensitive relapsed lymphoma (Complete or partial response), Hodgkin's or
non-Hodgkin's lymphoma, no evidence of "bulky" disease (> 10 cm in diameter);

10. Patients with chemo-sensitive CLL with persistent or recurrent disease after
fludarabine-based regimens, no evidence of "bulky" disease (> 10 cm in diameter)

11. Patients with poor prognosis multiple myeloma by cytogenetics (del13, del 17p,
t(1;14) or t(14;16) or hypodiploidy, with advanced disease (stage>/=2) and /or
relapsed after autologous stem cell transplant.

12. Patients with myelofibrosis (Lille >0, transfusion dependency, progression to blast
phase; however, in remission from AML) or CMML. These patients will be treated with
the reduced-intensity conditioning regimen (with melphalan 100mg/m2 and thiotepa 5
mg/kg regimen) and will be subject to the same stopping rule as the group >/= 55
years or with comorbidities.

13. Zubrod performance status 0-1 or Lansky PS greater or equal to 70%.

14. Available donor able to undergo a bone marrow harvest. For matched unrelated donor
transplants only: Peripheral blood stem cells may be collected if donor is
unavailable for bone marrow harvest or if adequate bone marrow cannot be collected.

15. Bilirubin
16. Serum creatinine clearance >/=50 ml/min (calculated with Cockroft-Gault formula);
Creatinine for children (whichever is less);

17. Diffusing capacity for carbon monoxide (DLCO) >/= 45% predicted corrected for
hemoglobin. For pediatric patients, if unable to perform pulmonary function, >/= 92%
oxygen saturation with pulse oximetry.

18. LVEF >/= 40%.

19. Patient or patient's legal representative, parent(s) or guardian should provide
written informed consent. Assent of a minor if participant's age is at least seven
and less than eighteen years.

Exclusion Criteria:

1. HIV positive; active hepatitis B or C

2. Patients with active infections. The PI is the final arbiter of the eligibility.

3. Liver cirrhosis with greater than grade 1 stage 1 inflammation/fibrosis

4. Uncontrolled CNS involvement by tumor cells

5. History of another primary malignancy that has not been in remission for at least 3
years. (The following are exempt from the 3-year limit: nonmelanoma skin cancer,
fully excised melanoma in situ [Stage 0], curatively treated localized prostate
cancer, and cervical carcinoma in situ on biopsy or a squamous intraepithelial lesion
on PAP smear.)

6. Positive Beta HCG test in a woman with child bearing potential defined as not
post-menopausal for 12 months or no previous surgical sterilization.

7. Inability to comply with medical therapy or follow-up