Patients with whole blood transfusion in the last days prior to entry to the study Patients who have had a transfusion within days of screening are NOT eligible for participation Must have transfusion-dependent anemia that meets the following criteria: For Parts A, B, and C, eligibility of participants who require blood transfusion before and after the start of the study treatment should be discussed by the Sponsor and investigator Whole blood transfusion in the last days prior to entry to the study Blood transfusion within weeks prior to screening Treatment for ? days complicated by either i. Development of a red blood cell transfusion requirement (at least units/month for months) ii. National Cancer Institute (NCI) CTCAE grade ? AEs of thrombocytopenia, anemia, hematoma, and/or hemorrhage while being treated with a dosage of < mg BID Non-leukocyte leukocyte-depleted whole blood transfusion within days of the date of the genetic sample collection. Absolute neutrophil count (ANC) <,/mm, pre-transfusion platelets <,/mm, or pre-transfusion hemoglobin <. mg/dL (the patient is required to have at least weeks free from blood transfusion, G-CSF and erythropoietin use prior to the hematology test) PLT < x/L (,/?L) and/or transfusion dependency (both criteria have to be fulfilled) AND/OR Advanced primary with impeding occlusion, perforation or bleeding, dependent on transfusion History of transfusion is acceptable and transfusions may be given to meet eligibility requirements Patients who require or are likely to require corticosteroid or other immunosuppressive drugs for intercurrent disease (any other significant medical problem related to or independent from the neuroblastoma or its treatment) while tentatively scheduled to receive treatment on this study are ineligible; the only exception is for patients known to require mg/kg or less of hydrocortisone (or an equivalent dose of an alternative corticosteroid) as premedication for blood product transfusion in order to avoid allergic transfusion reactions Patients should not have transfusion-dependent thrombocytopenia or bleeding disorders Whole blood transfusion in the last days prior to entry to the study FOR ALL PHASES (Ib AND II): Blood or platelet transfusion within days prior to treatment start Subjects who have unknown transfusion history Non-leukocyte depleted whole blood transfusion within days of the date of patient's start on the study Blood transfusion within days of consent No hematologic parameters for inclusion; transfusion-dependent patients are eligible and platelet counts should be maintained greater than ,/mm^ throughout cycles and Aplastic anemia with absolute neutrophil count (ANC) < , and transfusion dependent after failed immunosuppression therapy Blood transfusion or administration of growth factors within days prior to a blood draw being used to confirm eligibility Plts ? , - cannot be transfused (must be ? days from last plt transfusion) Blood transfusion within days of the blood draw being used to confirm eligibility History of Grade or higher blood transfusion incident according to US Biovigilance Network which refers to any transfusion followed by a major intervention (vasopressors, intubation, transfer to intensive care) to prevent death. Patients with transfusion-dependent anemia. Moderate or severe aplastic anemia defined by one of the following: peripheral blood neutrophils < . x ^/L; platelets < x ^/L or platelet transfusion dependence; reticulocytes < x ^/L in anemic patients or red cell transfusion dependence Plus any of the following: \r\n- Stroke or central nervous system event lasting more than hours\r\n- Magnetic resonance imaging (MRI) changes indicative of brain parenchymal damage\r\n- Magnetic resonance angiogram (MRA) evidence of cerebrovascular disease\r\n- Acute chest syndrome requiring exchange transfusion or hospitalization\r\n- Recurrent vaso-occlusive pain crisis (more than /year for the last years)\r\n- Stage I or II sickle lung disease\r\n- Sickle retinopathy\r\n- Osteonecrosis\r\n- Red cell alloimmunization (> antibodies) during long-term transfusion\r\n- Constellation of dactylitis in the first year of life and a baseline hemoglobin < g/dL and leukocytosis (> . x ^/mm^) in the absence of infection during the second year of life\r\n- History of invasive pneumococcal disease\r\n- Pitted red blood cell (RBC) count > .% during the first year of life\r\n- Abnormal transcranial Doppler\r\n- Transfusion dependence\r\n- Beta thalassemia major Transfusion dependent anemia with transfusion dependency of ? months History of at least one documented blood transfusion within months of enrollment Transfusion dependent alpha- or beta-thalassemia No specific hematologic parameters for study entry are required; transfusion-dependent patients are eligible and platelet counts should be maintained greater than ,/mm^ Subject received HMA for at least cycles and was still transfusion dependent (as defined in b below). TREATMENT: Patients must have >=. g/dL Hb and no blood transfusion in the past days to receive veliparib Presence of transfusion-dependent thrombocytopenia Presence of transfusion-dependent thrombocytopenia Condition (such as transfusion dependent anemia or thrombocytopenia), therapy, or laboratory abnormality that might confound the study results, or interfere with the patient's participation for the full duration of the study treatment. Excessive bleeding (above cc) identified prior to anastomosis formation with the need for intra-operative blood transfusion. Platelet count ? , cells/?L without transfusion support days before assessment. Subjects with transfusion-dependent thrombocytopenia are excluded. Platelet count ? , cells/?L, or ? , cells/?L in subjects with documented bone marrow involvement, and without transfusion support days before assessment. Subjects with transfusion-dependent thrombocytopenia are excluded. Must have symptomatic anemia untransfused with hemoglobin < . g/dL =< weeks prior to randomization or with red blood cells (RBC) transfusion dependence (i.e., >= units/month) confirmed for =< weeks before randomization\r\n* NOTE: For non-transfusion dependent patients (i.e., receiving < units/ weeks x weeks pre-study) who receive periodic transfusions, the mean week pre-transfusion hemoglobin should be used to determine protocol eligibility and response reference\r\n* For non-transfusion dependent patients, a minimum of pre-transfusion or un-transfused hemoglobin values are required Patients must be off all non-transfusion therapy for MDS for days prior to initiation of study treatment, including all types of growth factors; patients may receive hydrocortisone prophylactically to prevent transfusion reactions Presence of transfusion-dependent thrombocytopenia blood transfusion(s) prior to , Need for transfusion within days prior to the first dose of trial treatment Patients who have required a blood transfusion within days prior to study start Patients with transfusion-dependent thrombocytopenia are not eligible Patient who is growth factor or transfusion dependent Non-leukocyte depleted whole blood transfusion within days of the date of the pharmacogenetic sample collection. Previous major bleed (bleeding requiring transfusion of red blood cells) on LMWH Subjects may not have had a transfusion within days of screening assessment Blood transfusion within days of the blood draw being used to confirm eligibility Blood or albumin transfusion within days of the blood draw being used to confirm eligibility Presence of transfusion-dependent thrombocytopenia Patients who are platelet or red blood cell transfusion-dependent are eligible blood transfusion or hemopoietic factor therapy Presence of transfusion-dependent thrombocytopenia On a chronic transfusion program or planning on exchange transfusion during the study Blood or albumin transfusion within days prior to the blood draw being used to confirm eligibility Hematologic parameters must be assessed at least days after a prior transfusion, if any Blood transfusion within days prior to blood draw being used to confirm eligibility Aplastic anemia with absolute neutrophil count (ANC) < and transfusion dependent after they failed immunosuppression therapy Documented wish against transfusion for personal or religious beliefs Subjects who have unknown transfusion history for at least the weeks prior to screening No specific hematologic parameters for study entry are required; transfusion-dependent patients are eligible and platelet counts should be maintained greater than ,/mm^ History of major bleeding (requiring a blood transfusion ? units) not related to a tumor within the past months Chronic transfusion-dependent anemia with exposure to at least RBCT Thalassemia major or sickle cell disease requiring blood transfusion Previous blood transfusion ( days prior to genetic testing) Packed cell volume (PCV) >= (with or without transfusion) For IPSS intermediate- or low-risk MDS, participants must be transfusion dependent for red blood cells or platelets (as determined by instructional practices or local standard of care). Participants who are red blood cell transfusion dependent must also have failed erythropoiesis stimulating agents (primary resistance or relapse after a response) or have serum erythropoietin (EPO) levels > U/L.