Competition is at the heart of the European Union's (EU) roadmap in the field of transport. In rail transport, competition started late and took time to deploy. Just now, almost ten years after the 4th railway package, competition is becoming a Europe-wide affair rather than a collection of single and often small and short-lived national experiences. Today it is possible to draw a first picture of how open-access rail competition will be in the coming years, with a primary focus on the profitability of competition in high-speed market. The paper starts providing an overview of the forms that competition can take in the case of a non-cooperative game between two or three firm and an overview of the varied experiences of "on track" competition in Europe to date, on a country basis. Then the paper focuses on a recent case where the financial sustainability appears to be a serious issue: the entry of the Italian company Trenitalia in France, on the main country's route, the Paris-Lyon. The characteristics of the newcomer's business model are recalled, and its medium-term profitability is studied through a model, emphasising the role of access charges in it.