In this paper we present a history-friendly model of the changing vertical scope of computer firms during the evolution of the computer and semiconductor industries. The model is "history friendly", in that it attempts at replicating some basic, stylized qualitative features of the evolution of vertical integration on the basis of the causal mechanisms and processes which we believe can explain the history. The specific question addressed in the model is set in the context of dynamic and uncertain technological and market environments, characterized by periods of technological revolutions punctuating periods of relative technological stability and smooth technical progress. The model illustrates how the patterns of vertical integration and specialization in the computer industry change as a function of the evolving levels and distribution of firms' capabilities over time and how they depend on the co-evolution of the upstream and downstream sectors. Specific conditions in each of these markets - the size of the external market, the magnitude of the technological discontinuities, the lock-in effects in demand - exert critical effects and feedbacks on market structure and on the vertical scope of firms as time goes by