Large turbines are a synonym of more energy harvested from the wind, but also of increment in the costs. This dilemma has led many researchers on the field of wind energy to wonder about the optimum size for wind turbines concerning the lowest cost of energy. This project studies the optimum turbine size for offshore applications through the modeling of the costs of the components that have the largest contribution to the Levelized Production Cost (LPC). Since at different power ratings different power densities are optimal, the turbine size is considered in terms of the rotor diameter and the turbine rated power. Therefore, the cost models developed in this work are a function of these two parameters. To develop the cost models, classical scaling approaches are used along with an offshore wind farm design emulator tool. Regarding that the optimum turbine size is not the same for all situations, two case studies of offshore wind farms are established. These case studies contrast some of the relevant characteristics of an offshore wind farm as the power installed capacity, the distance from shore, the water depth, and the wind and wave environment. The optimal size for large, far offshore wind farms was found to be in the range of 10-13 MW, while it was around 5-7 MW for small near shore farms. The optimum turbine size depends mostly on the reduction in the cost of the O&M and the increment in the costs of the turbines and support structure as the turbine scale employed in the wind farm becomes larger. Finally, the blades cost appears to be a limiting factor for the increment in the rotor diameter for the large turbines scales.