Currently, we face an exponentially increasing interest in immersion, especially sensory-driven immersion, mainly due to the rapid development of ideas and business models centered around a digital virtual universe as well as the increasing availability of affordable immersive technologies for education, communication, and entertainment. However, a clear definition of 'immersion', in terms of established neurocognitive concepts and measurable properties, remains elusive, slowing research on the human side of immersive interfaces. To address this problem, we propose a conceptual, taxonomic model of attention in immersion. We argue (a) modeling immersion theoretically as well as studying immersion experimentally requires a detailed characterization of the role of attention in immersion, even though (b) attention, while necessary, cannot be a sufficient condition for defining immersion. Our broader goal is to characterize immersion in terms that will be compatible with established psychophysiolgical measures that could then in principle be used for the assessment and eventually the optimization of an immersive experience. We start from the perspective that immersion requires the projection of attention to an induced reality, and build on accepted taxonomies of different modes of attention for the development of our two-competitor model. The two--competitor model allows for a quantitative implementation and has an easy graphical interpretation. It helps to highlight the important link between different modes of attention and affect in studying immersion.