A Phase II Pilot Trial to Estimate Survival After a Non-total Body Irradiation (TBI) Based Conditioning Regimen in Patients Diagnosed With B-acute Lymphoblastic Leukemia (ALL) Who Are Pre-allogeneic Hematopoietic Cell Transplantation (HCT) Next-generation-sequence (NGS) Minimal Residual Disease (MRD) Negative

Inclusion Criteria for the Observational Arm: Any patient with ALL who undergoes Myeloablative HCT including any of the following: * Patients who are pre-HCT NGS-MRD positive. * Patients \<1 year old who are pre-HCT NGS-MRD negative. * Patients who are pre-HCT NGS-MRD negative (CR1/CR2) who received inotuzumab ozogamicin therapy before proceeding to HCT. * Patients who are pre-HCT NGS-MRD negative and will be receiving haploidentical HCT. * Patients who are pre-HCT NGS-MRD negative in CR2 with history of CNS relapse. * Patients who have received blinatumomab, but are \>CR2 prior to HCT. * Patients who have received CART-T cellular therapy, but are \>CR2 prior to HCT. * Patients with pre-HCT NGS-MRD negative in ≥ CR3. * Any T-ALL and MPAL patients undergoing first allogeneic HCT * Any patient who is pre-HCT NGS-MRD negative and eligible for participation in the treatment arm but family does not consent for treatment arm or treating physician believe it is in the patient best interest not to enroll on the treatment arm Inclusion Criteria for the Treatment Arm: * Pre-HCT NGS-MRD negative * Age ≥ 1 year and ≤ 25 years * Disease status: B-ALL in first (CR1) or second remission (CR2) * No prior allogeneic hematopoietic stem cell transplant. * Patients in CR1 or CR2 after blinatumomab treatment. * Patients in CR1 or CR2 after CAR-T cellular therapy. * Karnofsky Index or Lansky Play-Performance Scale ≥ 60 % on pre-transplant evaluation. Karnofsky scores must be used for patients \> 16 years of age and Lansky scores for patients \< 16 years of age. * Able to give informed consent if \> 18 years, or with a legal guardian capable of giving informed consent if \< 18 years. * Adequate organ function (within 4 weeks of initiation of preparative regimen), defined as: * Pulmonary: FEV1, FVC, and corrected DLCO must all be ≥ 50% of predicted by pulmonary function tests (PFTs). For children who are unable to perform for PFTs due to age, the criteria are: no evidence of dyspnea at rest and no need for supplemental oxygen. * Renal: Creatinine clearance or radioisotope GFR ≥ 60 mL/min/1.73 m2 or a serum creatinine based on age/gender. * Cardiac: Shortening fraction of ≥ 27% by echocardiogram or radionuclide scan (MUGA) or ejection fraction of ≥ 50% by echocardiogram or radionuclide scan (MUGA), choice of test according to local standard of care. * Hepatic: SGOT (AST) or SGPT (ALT) \< 5 x upper limit of normal (ULN) for age. Conjugated bilirubin \< 2.5 mg/dL, unless attributable to Gilbert's Syndrome. Exclusion Criteria: * CR2: exclude patients with history of CNS relapse (i.e. in CR2 with history of CNS isolated or combined relapse; CNS 2 will also be considered as CNS 3 for this purpose) from the treatment arm of study (can be enrolled on the observational arm). * Patients who have received inotuzumab treatment prior to allogeneic HCT are NOT eligible for the study treatment arm. Inotuzumab treatment may increase the risk of VOD/SOS for any allogeneic HCT recipient, but could potentiate the risk for with busulfan-based myeloablation (study-directed non-TBI conditioning). All inotuzumab-treated patients are eligible for the observational arm (HCT center standard of care). * Patients receiving non-myeloablative conditioning are not allowed on the observational arm (reduced toxicity conditioning with Flu/Mel/Thio is allowed on the observational arm). * Pregnant or lactating females are ineligible as many of the medications used in this protocol could be harmful to unborn children and infants. * Patients with HIV or uncontrolled fungal, bacterial or viral infections are excluded. Patients with history of fungal disease during induction therapy may proceed if they have a significant response to antifungal therapy with no evidence or minimal evidence of non-progressive disease remaining by CT evaluation. * Patients with active CNS leukemia or any other active site of extramedullary disease at the time of enrollment are not permitted. * T-ALL and MPAL patients are only allowed on the observational arm. * Patients with genetic disorders (generally marrow failure syndromes) prone to secondary AML/ALL with known poor outcome are not eligible (Fanconi Anemia, Kostmann Syndrome, Dyskeratosis Congenita, etc).