Allogeneic Hematopoietic Cell Transplantation for Peripheral T Cell Lymphoma

* INCLUSION CRITERIA-RECIPIENT: * Age \>=12 years * Diagnosis of PTCL, confirmed by NCI pathology review, that is relapsed or refractory to prior therapy, and/or PTCL where upfront allo HCT in first remission is reasonable (PIT score of intermediate-low risk or higher or supported by clinical practice guidelines) --ALK-positive ALCL patients will only be eligible if relapsed or refractory * At least one potential 7-8/8 HLA-matched related (excluding an identical twin) or unrelated donor (at HLA-A, -B, -C, and DR), or an HLA-haploidentical related donor, based on initial low resolution unrelated donor search and/or at least one biologically-related family member who has at least a 25% chance of being at minimum an HLAhaploidentical match and is potentially suitable to donate based on reported family history. HLA typing of potential donors and/or mutation testing does not need to be completed for eligibility. * Adequate end-organ function, as measured by: * For RIC: Left ventricular ejection fraction (LVEF) \>= 40% by 2D echocardiogram (ECHO) or MUGA, left ventricular shortening fraction \>= 20% by ECHO, or LVEF \>= 30% if the patient has radiologic evidence of aortic, renal, or coronary artery vasculitis. For IOC: LVEF \>= 30% by 2D ECHO or MUGA. * Pulmonary function tests: DLco (corrected for hemoglobin) and FEV1 \>= 40% of predicted for the RIC arm, and \>= 30% predicted for the IOC arm; or in pediatric patients, if unable to perform pulmonary function tests, there should be no evidence of dyspnea at rest, no requirement for supplemental oxygen, and oxygen saturation \>92% on room air. * Bilirubin \<= 3.0 mg/dL (unless due to Gilbert's syndrome or hemolysis) for patients receiving RIC and bilirubin \<= 5.0 mg/dL for patients receiving IOC (unless due to Gilbert s syndrome or hemolysis); ALT and AST \<= 10 x ULN for patients receiving RIC or IOC. Patients who are above these bilirubin, ALT, or AST thresholds may be eligible for the RIC or IOC arm if evaluated by a hepatologist who deems the liver function test abnormalities to be potentially disease related, either because of direct involvement by PTCL, due to an associated process such as hemophagocytic lymphohistiocytosis, or as sequelae of prior chemotherapy that is thought to improve with time. * Estimated creatinine clearance of \>= 50 mL/min/1.73 m\^2, calculated using eGFR in the clinical lab for adults and the Schwartz formula for pediatrics. * Karnofsky (adults) or Lansky (children) performance status of \>= 50% or ECOG performance status of 2 or less for the RIC arm and Karnofsky (adults) or Lansky (children) \>= 30% or ECOG performance status of 3 or less for the IOC arm * Ability of subject or parent/guardian to understand and the willingness to sign a written informed consent document * Not pregnant or breastfeeding. * As therapeutic agents used in this trial may be harmful to a fetus, individuals of childbearing potential and individuals who can father children must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for at least one year post-allo HCT. EXCLUSION CRITERIA-RECIPIENT: * Patients who are receiving any other investigational agents, with the exception of virus-specific cytotoxic T-cells for the treatment of viral infection/reactivation prior to allo HCT. * Prohibitive allergy to a study drug or to compounds of similar chemical or biologic composition of the agents (e-ATG, steroids, cyclophosphamide, busulfan, pentostatin, sirolimus, MMF, filgrastim or biosimilar drug) used in the study * Lack of central venous access potential * Active psychiatric disorder which is deemed by the PI to have significant risk of compromising compliance with the transplant protocol or which does not allow for appropriate informed consent INCLUSION CRITERIA-RELATED DONOR: -Related donor deemed suitable and eligible, and willing to donate, per clinical evaluations who are additionally willing to donate blood and/or peripheral blood stem cells for research. Related donors will be evaluated in accordance with existing Standard Policies and Procedures for determination of eligibility and suitability for clinical donation. EXCLUSION CRITERIA-RELATED DONOR: None INCLUSION CRITERIA (UNRELATED DONOR): -Unrelated donors will be evaluated in accordance with existing NMDP Standard Policies and Procedures, available at: http://bethematch.org/About-Us/Global-transplantnetwork/ Standards/, except for the additional requirement of EBV serostatus testing for clinical purposes of donor selection. Note that participation in this study is offered to all unrelated donors but not required for clinical donation, so it is possible that not all unrelated donors will enroll on this study. Unrelated donors only enroll if they contribute research specimens, which is optional. EXCLUSION CRITERIA (UNRELATED DONOR): -Unrelated donors: failure to qualify as a National Marrow Donor Program (NMDP) donor per current NMDP Standards, available at: http://bethematch.org/About-Us/Globaltransplant- network/Standards/. Exceptions to donor eligibility (e.g. foreign travel, tattoos) do not automatically exclude the donor and will be reviewed by the PI.