In recent years, several criteria have been identified for the selection of hepatocellular cancer (HCC) patients waiting for liver transplantation (LT). These criteria, like the Milan Criteria, are also the foundation of models for predicting the risk of relapse after transplantation. However, these models are severely limited in considering many variables and their non-linear interactions. The starting point is TRAIN-AI, based on the DeepSurv neural network: a Cox proportional hazards model. This model was developed starting from an International Cohort which will also be the main dataset of this study. Furthermore new deep learning models based on hazard rate parametrization and probability mass function (PMF) parametrization are proposed and compared, performing an appropriate hyperparameter tuning for each network.