Patient with liver failure waiting for liver transplantation are often hospitalized and commonly supported in an intensive care unit prior to surgery. These patients are sick, and in addition to the complications of a failing liver, other organs such as the kidneys often fail as well. As a consequence, these patients are at an increased risk for complications related to their kidney failure during their liver transplantation procedure. One potential method to diminish the risk of these complications is to provide dialysis support to these patients during their liver transplantation in the operating theater in the form of continuous renal replacement therapy (CRRT). While this is increasingly being performed and is theoretically appealing, there is very little information to support this practice. In addition, the use of CRRT during surgery is not entirely without risk. The investigators have performed two preliminary studies on the use of CRRT during liver transplantation and our data would strongly support the need to conduct further higher-quality studies to better evaluate its feasibility, safety and usefulness. Our proposed study is for a randomized trial comparing the use of CRRT during surgery with standard supportive care in sick patients with liver failure scheduled to receive a liver transplantation.