Despite acknowledgements that migration depends on human–material practices, research into migrant materialities has often focused on limited spatiotemporal frames and the relation of objects to (inter)personal concerns. Taking everyday interactions with materials as of inherent interest, I examine how thinking topologically about multiple spaces helps to trace migrants’ relationships to changing groups of objects. After introducing Mol and Law's concepts of regional, network and fluid space, I discuss three types of networks with diverse relations to them – networks of home, for travel, and of use. Though networks of home are important to migrants, and can remain intact while travelling across regions, they also demonstrate considerable fluidity when interacting with other networks, which themselves affect adaptation and everyday practices. Supported by examples from Hong Kong return migrants, I show how managing multiple material networks, each with multiple spatial relations, is central to being a migrant.