Donor Umbilical Cord Blood Transplant By Injection Into the Bone Marrow in Treating Patients With Hematologic Cancer

Inclusion Criteria:

* Acute myeloid leukemia (AML): high risk CR1
* Acute lymphocytic leukemia (ALL): high risk CR1 \[t(9;22), t (1:19), t(4;11) or other MLL rearrangements\] or \> 1 cycle to obtain CR; CR2+. All patients must be in CR as defined by hematological recovery, AND \<5% blasts by light microscopy within the bone marrow with a cellularity of ≥15%.
* Chronic myelogenous leukemia (CML) excluding refractory blast crisis. To be eligible in first chronic phase (CP1) patient must have failed or be intolerant to imatinib mesylate.
* Myelodysplasia (MDS) IPSS Int-2 or High risk (i.e. RAEB, RAEBt) or refractory anemia with severe pancytopenia or high risk cytogenetics.
* Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL), marginal zone B-cell lymphoma or follicular lymphoma that have progressed after at least two prior therapies. Patients with bulky disease (nodal mass greater than 5 cm).
* Lymphoplasmacytic lymphoma, mantle-cell lymphoma, prolymphocytic leukemia are eligible after initial therapy in CR1+ or PR1+.
* Large cell NHL \> CR2/\> PR2. Patients in CR2/PR2 with initial short remission (\<6 months) are eligible.
* Lymphoblastic lymphoma.
* Multiple myeloma beyond PR2.
* Karnofsky performance status (PS) 90-100% (adults)
* Lansky PS 50-100% (children)
* Acceptable organ function

Exclusion Criteria:

* Active infection at time of transplantation
* History of HIV infection
* Pregnant or breast feeding.
* Chemotherapy refractory large cell and high grade NHL (ie progressive disease after \> 2 salvage regimens)
* Extensive prior therapy including \> 12 months alkylator therapy or \> 6 months alkylator therapy with extensive radiation.
* Diffuse myelofibrosis of BM (bone marrow) (any severity) regardless of primary diagnosis (focal fibrosis acceptable provided it involves \< 20% of BM volume).
* History of pelvic irradiation.