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 grad…