Abstract In this paper, we examine in a systematic way the problem of decentralization in an economy with all types of externalities. We show that decentralization with artificial markets requires strong convexity assumptions which are typically not fulfilled for negative externalities on producers. A milder form of decentralization with taxation is shown to obtain under weaker convexity assumptions. A new example is given to explain the role of a non-interiority assumption. Finally, new types of non-convexities are described and the problem of rights to externalities is clearly defined in the framework of this general theory.