Many corporations are large, powerful, and wealthy. There are massive shortfalls of global justice, with hundreds of millions of people in the world living below the threshold of extreme poverty, and billions more living not far above that threshold. Where injustice and needs shortfalls must be remediated, we often look towards agents’ capabilities to determine who ought to bear the costs of rectifying the situation. The combination of these three claims grounds what I call a ‘linkage-based’ account of why corporations (...) have demanding positive duties to the global poor. In this paper, I put forward a distinctive linkage-based account of corporations’ positive duties centred on the idea of dependence and the importance of meeting agents’ core needs. In addition to outlining and defending this account, I will show that we can utilise its basic conceptual components to make headway on questions that have received insufficient attention in the business ethics literature; specifically, we can say something substantive about the weighting of needy agents’ competing claims to assistance, and about the limits to the demands that can be lodged against corporations on the basis of others' unmet needs. Having integrated considerations of duties' grounding, their comparative weight, and the limits of their demandingness into a single account of corporate positive duty, I conclude by discussing a challenge to attributing to corporations duties owed to the worst-off amongst the global poor. (shrink)