Current technical capabilities of mobile technologies are consolidating the interest in developing context-aware Augmented/Mixed Reality applications. Most of these applications are designed based on the Window-on-the-World (WoW) interaction paradigm. A significant decrease in cost of projection technology and advances in pico-sized projectors have spurred applications of Projective Augmented Reality. This research has focused mainly on technological development. However, there is still a need to fully understand its communicational and expressive potential. Hence, we define a conceptual paradigm that we call World-as-Support (WaS). We compare the WaS and WoW paradigms by contrasting their assumptions and cultural values, as well as through a study of an application aimed at supporting the collaborative improvisation of sitespecific narratives by children. Our analysis of children's understanding of the physical and social environment and of their imaginative play allowed us to identify the affordances, strengths and weaknesses of these two paradigms.