The researchers are doing this study to compare 2 different GVHD prevention (prophylaxis) approaches. The researchers will see which approach is good or more effective at preventing chronic GVHD until 1 year after allogeneic hematopoietic stem cell transplantation (allo-HCT).

Inclusion Criteria:

• Patients ≥18- years-old at time of consent

• Diagnosis: hematologic malignancy in morphologic remission (blasts <5%, no evidence of extramedullary disease in AML or MDS). Patients with CR with incomplete count recovery (CRp or CRi) or minimal residual disease are allowed. Patients with lymphoma must have a complete or partial response

• Donor: related or unrelated 7-8/8 HLA-matched or related haploidentical

• Karnofsky score ≥ 70%

• Female subjects of childbearing potential (<50 years old) have a negative serum or urine pregnancy test. Females of childbearing potential are defined as females without prior hysterectomy or who have had any evidence of menses in the past 12 months.

  °Sexually active females of childbearing potential enrolled in the study must agree to consistently use two forms of accepted methods of contraception during the course of the study and for 3 months after their last dose of the study drug. Effective birth control includes: *Intrauterine device (IUD) plus one barrier method *Stable doses of hormonal contraception for at least 3 months (e.g., oral, injectable, implant, transdermal) plus one barrier method *2 barrier methods. Effective barrier methods are male or female condoms, diaphragms, and spermicides (creams or gel that contain a chemical to kill sperm); or * A vasectomized partner.

• For male subjects who are sexually active and who are partners of females of childbearing potential: Agreement to use two forms of contraception as per above and to not donate sperm during the treatment period and for at least 3 months after the last dose of study drug

Exclusion Criteria:

• Recipient of CD34+ selected or engineered stem cell graft
• Treatment with in vivo T cell depletion (e.g. anti-thymocyte globulin)
• Patients with an active secondary malignancy or prior malignancy requiring systemic therapy within the past 5 years. Exceptions include adequately treated localized non-melanoma skin cancer (basal cell carcinoma and squamous cell carcinoma), as well as localized prostate cancer considered low risk and stable under treatment or surveillance.
• Severely impaired renal function defined by serum creatinine > 2mg/dL, renal dialysis requirement.
• Use of investigational agent within 14 days pre-HCT
• Evidence of current uncontrolled cardiovascular conditions, including uncontrolled hypertension, uncontrolled cardiac arrhythmias, symptomatic congestive heart failure, unstable angina, or myocardial infarction within the past 6 months
• Uncontrolled psychiatric illness
• Female patient who is pregnant or breastfeeding
• Known allergy or sensitivity to ruxolitinib

Memorial Sloan Kettering Cancer Center supports the international committee of medical journal editors (ICMJE) and the ethical obligation of responsible sharing of data from clinical trials. The protocol summary, a statistical summary, and informed consent form will be made available on clinicaltrials.gov when required as a condition of Federal awards, other agreements supporting the research and/or as otherwise required. Requests for deidentified individual participant data can be made following one year after publication and for up to 36 months later. Deidentified individual participant data reported in the manuscript will be shared under the terms of a Data Use Agreement and may only be used for approved proposals. Requests may be made to: crdatashare@mskcc.org.