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This paper extends the analysis of infinite dimensional vector autoregressive (IVAR) models proposed in Chudik and Pesaran to the case where one of the variables or the cross-section units in the IVAR model is dominant or pervasive. It is an important extension from empirical as well theoretical perspectives. In the theory of networks a dominant unit is the centre node of a star network and arises as an efficient outcome of a distance-based utility model. Empirically, the extension poses a number of technical challenges that goes well beyond the analysis of IVAR models provided in Chudik and Pesaran. This is because the dominant unit influences the rest of the variables in the IVAR model both directly and indirectly, and its effects do not vanish as the dimension of the model (N) tends to infinity. The dominant unit acts as a dynamic factor in the regressions of the non-dominant units and yields an infinite order …