Inclusion Criteria:4.1. Recipient Inclusion Criteria

4.1.1. Male or female recipients must have histopathologically confirmed diagnosis of hematological or lymphatic malignancy in one of the following categories: 4.1.1.1. Acute myeloid leukemia (in relapse or primary refractory disease) 4.1.1.2. Acute leukemia (in first remission with poor risk factors and molecular prognosis; AML with -5,-7, t(6;9), tri8, -11 and ALL with Phil+ t(9;22),(q34;q11.2), and t(4:11)(q21;23) 4.1.1.3. Chronic myelogenous leukemia (accelerated, second chronic phase) 4.1.1.4. Myelodysplastic syndrome (in high and high intermediate risk categories) 4.1.1.5. Non-Hodgkin's lymphoma ) 4.1.1.6. Refractory CLL

4.1.2. The recipient must be < 50 years old at time of registration.

4.1.3. The recipient must have a related donor genotypically HLA-A, B,C and DRB1, DQ loci haploidentical to the recipient (but differing for 2-3 HLA alleles on the unshared haplotype in the GvHD direction) and no HLA matched sibling or matched unrelated donor is identified.

4.1.4. Recovery from prior therapy, chemotherapy, or radiotherapy, as defined by: 4.1.4.1. ECOG performance status < 2

4.1.5. Adequate cardiac and pulmonary function (LVEF > 45%, DLCO > 50% corrected for hemoglobin)

4.1.6. Serum creatinine < 1.5 mg/dL or creatinine clearance > 50 ml/min for those above serum creatinine of 1.5; serum bilirubin < 2.0 mg/dL; ALT < 2x ULN (unless secondary to disease)

4.1.7. Females of childbearing potential must have a negative serum or urine beta-HCG test within three weeks of registration. Additionally, patients will be required to take adequate contraceptive measures.

4.1.8. No prior cancer within five years with the exception of surgically cured non-melanoma skin cancer or in situ cancer of the cervix

4.1.9. No prior myeloablative therapy or transplant

4.1.10. The recipient and/or the recipient's legal guardian must have been informed of the investigational nature of this study and have signed a consent form which is in accordance with Federal guidelines and the guidelines of the Stanford IRB.

4.2. Recipient Exclusion Criteria

4.2.1. The recipient is a suitable candidate for autologous transplantation.

4.2.2. Participation in other clinical trials which involve investigational drugs or devices that might influence the endpoints of this study

4.2.3. Evidence of active hepatitis or cirrhosis

4.2.4. HIV positive

4.2.5. History of invasive aspergillosis; presence of any other active, uncontrolled bacterial, viral or fungal infection

4.2.6. Uncontrolled CNS involvement

4.2.7. Documented allergy to murine proteins or iron dextran

4.2.8. The recipient is a lactating female or, if of child-bearing potential, is unwilling to implement adequate birth control.

4.2.9. The recipient has a medical problem or neurologic/psychiatric dysfunction which would impair his/her ability to be compliant with the medical regimen and to tolerate transplantation or would prolong hematologic recovery which in the opinion of the principal investigator would place the recipient at unacceptable risk.

4.3. Donor Inclusion Criteria

The donor must be examined and have specific tests performed according to existing institutional guidelines to evaluate his/her candidacy as a donor including the following:

4.3.1. Age < 60 years and weight greater than 25 kg.

4.3.2. Medical history and physical examination confirm good health status as defined by institutional standards

4.3.3. Seronegative for HIV Ag, HIV 1+2 Ab, HTLV I/II Ab, HBsAg, HBcAb (IgM and IgG), HCV Ab, RPR for syphilis within 30 days of apheresis collection

4.3.4. Genotypically haploidentical as determined by HLA typing

4.3.5. Female donors of child-bearing potential must have a negative serum or urine beta-HCG test within three weeks of mobilization

4.3.6. Capable of undergoing leukapheresis, have adequate venous access, and be willing to undergo insertion of a central catheter should leukapheresis via peripheral vein be inadequate

4.3.7. Agreeable to second donation of PBPC (or a bone marrow harvest) should the patient fail to demonstrate sustained engraftment following the transplant.

4.3.8. The donor, or legal guardian greater than 18 years of age, must have been informed of the investigational nature of this study and have signed a consent form in accordance with Federal Guidelines and the guidelines of the Stanford IRB.

4.3.9. The prospective donor will be screened for CMV seroreactivity and a seronegative donor will be utilized if available when the patient is seronegative. Otherwise the donor will be selected on the ability of NK cell alloreactivity based upon HLA typing results and donors who are capable of NK cell alloreactivity will be used preferentially.

Exclusion Criteria:4.2. Recipient Exclusion Criteria

4.2.1. The recipient is a suitable candidate for autologous transplantation.

4.2.2. Participation in other clinical trials which involve investigational drugs or devices that might influence the endpoints of this study

4.2.3. Evidence of active hepatitis or cirrhosis

4.2.4. HIV positive

4.2.5. History of invasive aspergillosis; presence of any other active, uncontrolled bacterial, viral or fungal infection

4.2.6. Uncontrolled CNS involvement

4.2.7. Documented allergy to murine proteins or iron dextran

4.2.8. The recipient is a lactating female or, if of child-bearing potential, is unwilling to implement adequate birth control.

4.2.9. The recipient has a medical problem or neurologic/psychiatric dysfunction which would impair his/her ability to be compliant with the medical regimen and to tolerate transplantation or would prolong hematologic recovery which in the opinion of the principal investigator would place the recipient at unacceptable risk.

4.4. Donor Exclusion Criteria

4.4.1. Evidence of active infection (including urinary tract infection, or upper respiratory tract infection) or hepatitis (on screening )

4.4.2. Medical, physical or psychological reason which makes the donor unlikely to tolerate or cooperate with growth factor therapy and leukapheresis.

4.4.3. Factors which place the donor at increased risk for complications from leukapheresis or G-CSF therapy.

4.4.4. Lactating female or, if of child-bearing potential, is unwilling to implement adequate birth control.

4.4.5. HIV positive.