Histologically confirmed, biopsy-proven diagnosis of DLBCL, BCLu, HGBCL, or TiNHL. Richter's transformation from Chronic Lymphocytic Leukemia (CLL) is not eligible. Richter's transformation from CLL History of Richter's transformation from CLL CLL WITH RICHTER's TRANSFORMATION (ARM C) ONLY Presence of more than 55% pro-lymphocytes in peripheral blood; patients with Richter's transformation are not excluded Richter's transformation confirmed by biopsy Chronic lymphocytic leukemia and Richter's transformation, and prolymphocytic leukemia (NHL subjects) Richter transformation. Richter transformation Confirmed diagnosis of B-cell Chronic Lymphocytic Leukemia or Richter's Transformation Participants with CLL or DLBCL who have Richter's Transformation Patients with active Richter's syndrome (>10% large B-cells in marrow). Richter's transformation (DLBCL arising in the setting of prior chronic lymphocytic leukemia) or Primary Mediastinal B cell Lymphoma (PMBCL) History of Richter's transformation or prolymphocytic leukemia Patients with known Richter's transformation which is progressive and is deemed to require immediate chemotherapy (history of Richter's transformation is not an exclusion); patients with prolymphocytic leukemia (prolymphocytes in blood >55%) Diagnosis of CLL without the following: Richter's transformation, prolymphocytic leukemia (PLL), small lymphocytic lymphoma (SLL) If the subjects has Richter's Syndrome (RS), the diagnosis is confirmed by biopsy and is immunohistologically characterized as transformation to DLBCL. Known prolymphocytic leukemia or history of, or currently suspected, Richter's syndrome. Known prolymphocytic leukemia or history of, or currently suspected, Richter's syndrome. Richter syndrome Patients with chronic non-T-cell-based lymphocytic leukemia are eligible if they have isolated lymphocytosis (Rai stage O) on the condition that they do not require systemic treatment for their disease [\B\ symptoms, Richter's transformation, lymphocyte doubling time (<6 months) and they do not have lymphadenopathy of hepatosplenomegaly]. Subject has developed Richter's transformation confirmed by biopsy Richter's Syndrome and Prolymphocytic Leukemia Transformation only: biopsy proven DLBCL Richter's transformation or prolymphocytic leukemia transformation. History of Richter's transformation or prolymphocytic leukemia Subjects with Richter's transformation Known central nervous system leukemia/lymphoma or Richter's transformation CLL patients with transformed disease (Richter's transformation) are ineligible for enrollment on this study Disease transformation [i.e. Richter's Syndrome (lymphomas) or prolymphocytic leukemia] Disease transformation (active) (ie, Richter's Syndrome, prolymphocytic leukemia) Richter's transformation or prolymphocytic leukemia Richter's transformation, arising in the setting of prior CLL, documented by histologically confirmed lymphoma, including large B-cell and immunoblastic variants. Active disease transformation (ie, Richter's Syndrome); subjects with Richter's Syndrome that has resolved > 2 years from signing the ICD are eligible. Co-existent diffuse large B-cell lymphoma (Richter's transformation) Patients with chronic lymphocytic leukemia, prolymphocytic leukemia, or Richter's transformation who are eligible for allogeneic transplantation and are not eligible for protocols of higher priority. Known transformation of CLL (e.g. Richter's). Documented prolymphocytic leukemia (prolymphocytes more than 55% in the blood) or Richter's transformation