This dissertation focuses broadly on how groups own a shared history, whether through doing so by legal property rights or by intellectual or cognitive ownership. It uses examples of material that by its nature is an assemblage from a variety of groups, and indeed at the time, different worlds: ships and their associated cargo between the ‘Old World’ and the ‘New World’ from the 16th to the 19th century. Because these wrecks carry the material of multiple nations both past and present, and due to their locations in international water, ships offer unique opportunities for stakeholders to emerge beyond the boundary of the nation state, which often defines archaeological ownership. Rather than shipwrecked assemblages or ‘treasure’ representing just one category of value, be it monetary, national, or educational, these ‘amphibious’ pieces link both land and sea, public and private property, and tangible and intangible heritage. Using interviews with curators and experts in the field of underwater cultural heritage, a case study, and two databases of shipwrecks with their associated material and ownership battles, the discussion will reveal the tension of owning colonial cargo, and the need for a solution that calls for co-owning hybridity.