To achieve these goals a 2-stage accrual design will be used with a maximum accrual goal of 10 patients. Initially 5 patients will be entered on-study. If more than one patient experiences grade 4 hemorrhaging/bleeding following OLT the trial will be closed and sorafenib will not be considered safe and/or feasible. If no patient experiences this event 5 additional patients will be enrolled. At the end of the study sorafenib will be considered safe and feasible in this setting if no patient experience grade 4 hemorrhaging/bleeding following transplant. With this design, and assuming at least 3 of the 5 patients in each cohort undergo OLT, the likelihood of stopping early is <.04 if the underlying risk hemorrhages/bleeding are low (<5% each) whereas there is a >.42 chance of early termination if the risks are substantial (e.g. >.20 likelihood of dose limiting toxicity and >.30 likelihood of >grade 4 hemorrhages/bleeding). Overall the likelihood of accepting or not accepting sorafenib as safe and feasible are >.84, and <.16, respectively under these conditions.