If someone has acute liver failure and needs a transplant, how does the health team find a liver so quickly?

They don't always...: Sadly, many more people can benefit from a liver transplant than there are transplants to be had. So, patients are stratified/triaged based on urgency of need, reason for liver failure, likelihood of post-operative compliance (take drugs, medical follow-up, avoid alcohol, etc.), home location, affordability, ; more. Please help by checking the donor box when getting/renewing your driver's license.