Emissions trading is becoming more and more important. So far, emission rights have almost always been allocated free of charge. This in turn has started a discussion of possible dominant market positions. In this context, existing literature either simply assumed that such a position exists and analysed the implication or determined market shares based on entitlements allocated to individual players. With regard to the second line of literature we argue that this approach is not satisfactory and propose an approach based on 1) initial allocation together with 2) marginal abatement costs curves and 3) business-as-usual emissions. Together with a given market price these three factors allow a determination of market shares. Based on competition law systems in the US, the EU and Japan we discuss possible relevant market shares that may provide the floor for dominant market positions. Applied to the international climate regime we conclude that certain allocation rules that might be perceived as “fairâ€ may imply possible dominant market positions for Parties that would have to reduce their emissions considerably.