This chapter explores the articulation of mobility and state power that operates at Ponte Galeria by tracking the movements of ospiti between national boundaries, legal grammars and exclusionary spaces. Together, the above mentioned movements call attention to the limit conditions of subjectivity for people already existing at the edges of life. It reveals the detention centre to be, paradoxically, both a space of statelessness and a space where Italian state power operates in full force. The chapter concludes with a meditation on the ambiguities of hospitality and the ethical consequences of the relationship between the ospite-as-subject and the powers held in tension in the grey-zone of a place - a heterotopia - such as the centre. It suggests that hospitality and the subjects it interpellates, the becoming-ospiti, advance the emancipatory potentials of mobility and open up possibilities for more empathic and hopeful futures for all.