Scholars have suggested that ‘home’ states of transnational corporations (TNCs) have a legal duty to protect against human rights abuses occurring in ‘host’ states that may be breached by failure to regulate TNCs’ extraterritorial activities. This article challenges the claim that such a duty of home states to regulate TNCs’ extraterritorial human rights impacts can be said currently to exist as a matter of law. The article first summarizes the general structure of arguments made in favour of such a ‘home state duty to regulate’. It then considers the foundations and meanings of extraterritorial jurisdiction in public international law and international human rights law, requirements and conditions of attribution and state responsibility for the conduct of non-state actors, and the scope and limits of ‘positive obligations’ to ensure the effective enjoyment of human rights, domestically and extraterritorially, as they relate to prevention of human rights abuses by TNCs.