The liver has a great capacity to regenerate after partial hepatectomy but it is not always successful. Liver cells proliferate to replace the lost metabolic capacity. This paper introduces two mathematical models based on ordinary differential equations for the regeneration of the liver after partial hepatectomy. The cell cycle has three cell types, quiescent, primed and replicating, and the main driver of the cycle is the deficit in the metabolic capacity of the liver. The analysis of the model is limited by the complicated expressions for the steady solutions and their stability. Numerical simulations are done to study different scenarios. A global sensitivity analysis shows that the biggest indices correspond to the failure rates of the process. The paper also gives realizations for different values of the parameters and shows that the regeneration process is successful for many ranges of the parameter values.