COVID-19-related controversies concerning the allocation of scarce resources, travel restrictions, and physical distancing norms each raise a foundational question: How should authority, and thus responsibility, over healthcare and public health law and policy be allocated? Each controversy raises principles that support claims by traditional wielders of authority in “federal” countries, like federal and state governments, and less traditional entities, like cities and sub-state nations. No existing principle divides “healthcare and public law and policy” into units that can be allocated in intuitively compelling ways. This leads to puzzles concerning (a) the principles for justifiably allocating “powers” in these domains and (b) whether and how they change during “emergencies.” This work motivates the puzzles, explains why resolving them should be part of long-term responses to COVID-19, and outlines some initial COVID-19-related findings that shed light on justifiable authority allocation, emergencies, emergency powers, and the relationships between them.