Abstract Heritage languages (HL), like other contact varieties, are subject to considerable transfer. However, the question remains of whether structures are really transferred from one language to another. Two case studies, one about datives in heritage Spanish, and the other about resultatives in heritage Ambon Malay, serve as a basis for discussion around the nature of structural transfer in HLs. The main conclusion is that structural transfer can be characterized as a redistribution of already available structures, driven by lexical and conceptual properties. In order to account for this, we explain structural transfer in terms of cross-linguistic activation in a psycholinguistic model inspired by Hartsuiker et al. (2004).