Inclusion Criteria:

- HIV-1 infection, as documented by a rapid HIV test or any FDA-Approved HIV-1 Enzyme
or Chemiluminescence Immunoassay (E/CIA) test kit and confirmed by Western Blot at
any time prior to study entry. HIV antigen, plasma HIV-1 RNA, or a secondary
antibody test by a method other than rapid HIV and E/CIA is acceptable as an
alternative test. Alternatively, if a rapid HIV test or any FDA-Approved HIV-1
Enzyme or Chemiluminescence Immunoassay (E/CIA) test is not available, two HIV-1 RNA
values greater than or equal to 2000 copies/mL at least 24 hours apart performed by
any laboratory that has CLIA certification, or its equivalent, may be used to
document infection.

- Patients must be willing to comply with effective Antiretroviral Therapy.

- Patients must be greater than or equal to 15 years of age.

- Hematological malignancy associated with a poor prognosis with medical therapy alone.
Diagnoses to be included: a)Patients with the diagnosis of Acute Myeloid or
Lymphocytic Leukemia (AML or ALL) in first or second complete remission; b)Patients
with advanced myelodysplastic syndromes (MDS), including those with International
Prognostic Scoring System (IPSS) Int-2 and high-risk disease with less than 10
percent marrow blasts and no circulating myeloblasts after most recent therapy.
Patients with acute leukemia that develops from a pre-existing MDS must meet the
inclusion criteria for patients with AML detailed above; c)Hodgkin Lymphoma beyond
first remission achieving at least a partial response to most recent therapy with no
evidence of progression prior to transplant; d)Non-Hodgkin Lymphoma beyond first
remission achieving at least a partial response to most recent therapy with no
evidence of progression prior to transplant.

- Donor/recipient HLA matching: a) Related donor: must be an 8/8 match at HLA-A, -B,
-C, (serologic typing or higher resolution) and -DRB1 (at high resolution using DNA
based typing). A 7/8 related donor match is permitted only if an 8/8 unrelated donor
cannot be identified; b) Unrelated donor: must be a 7/8 or 8/8 match at HLA-A, -B,
-C, and -DRB1 (at high resolution using DNA based typing).

- Patients with adequate organ function as measured by: a)Cardiac -Left ventricular
ejection fraction at rest greater than or equal to 40 percent demonstrated by MUGA or
echocardiogram. Patients with known heart disease must have a functional status no
worse than American Heart Association Class I defined as patients with cardiac
disease but without resulting limitation of physical activity. Ordinary physical
activity does not cause undue fatigue, palpitation, dyspnea, or anginal pain;
bi)Hepatic - Total Bilirubin less than 2.0 mg/dL (except for isolated
hyperbilirubinemia attributed to Gilbert syndrome or antiretroviral therapy as
specified in the protocol Appendix E) and ALT and AST less than 5x the upper limit of
normal; bii)Concomitant Hepatitis - Patients with chronic hepatitis B or C may be
enrolled on the trial providing the above bilirubin and transaminase criteria are
met. In addition, there must be no clinical or pathologic evidence of irreversible
chronic liver disease, and there must be no active viral replication as evidenced by
an undetectable hepatitis viral load by a PCR-based assay; c)Renal-Creatinine
clearance (calculated creatinine clearance is permitted) greater than 40 mL/min;
d)Pulmonary: DLCO, FEV1, FVC greater than or equal to 45 percent of predicted
(corrected for hemoglobin).

- Signed Informed Consent

Exclusion Criteria:

- Karnofsky/Lansky performance score less than 70 percent.

- Active CNS malignancy; however, patients with a history of positive CSF cytology that
has become negative with intrathecal chemotherapy are eligible.

- Uncontrolled bacterial, viral or fungal infection (currently taking medication and
with progression or no clinical improvement).

- Active CMV retinitis or other CMV-related organ dysfunction.

- AIDS related syndromes or symptoms that pose a perceived excessive risk for
transplantation-related morbidity as determined by the principal investigator.

- Untreatable HIV infection due to multidrug antiretroviral resistance. Patients with
a detectable viral load greater than 750 copies/ml should be evaluated with an HIV
drug resistance test (HIV-1 genotype). The results should be included as part of the
Antiretroviral Review. This Review Committee will make the final determination as to
whether HIV viremia could potentially be suppressed with alternate antiretroviral
therapy.

- Pregnant (positive β-HCG) or breastfeeding.

- Fertile men or women unwilling to use contraceptive techniques from the time of
initiation of mobilization until six-months post-transplant.

- Prior allogeneic HCT.

- Patients with psychosocial conditions that would prevent study compliance and
follow-up, as determined by the principal investigator.

- T-cell depletion (including ATG or alemtuzumab) is not allowed.

- Use of cord blood as the source of hematopoietic cells is not allowed.