This article investigates recent transformations in global capitalism’s political economy as it relates to the evolution of globally integrated production and exchange apparatuses, such as platforms, enabled through technological advances in computational infrastructures. These infrastructures are explicable in terms of the model of the Stack, understood as an accidental mega-structure of the contemporary platform economy that is integrating previously detached circulation and accumulation structures. The Stack is introduced as an integrative model of a multi-layered political economic system that allows us to understand and explain recent developments in global capitalism. Focus is thereby given to intensified real abstraction of labour induced by the capitalist appropriation of planetary-scale computation, and the associated rise of platform sovereignty in opposition to the traditional sovereignties of states and markets. Building on the model of the Stack, we set in relation different perspectives on recent capitalist development in terms of planetary-scale computation: transnational informational capitalism, cognitive capitalism, intellectual monopoly capitalism and techno-feudalism. Thereby we highlight aspects of value creation as well as rent-seeking through the model of the Stack.