An edge location can include data plane capacity controlled at least partly by a control plane of a nearby availability zone of the provider network. As such, an availability zone group can include a “parent” availability zone and any “child” edge locations homed to (e.g., controlled at least partly by the control plane of) the parent availability zone. Certain limited control plane functionality (e.g., features that require low latency communication with customer resources, and/or features that enable the edge location to continue functioning when disconnected from the parent availability zone) may also be present in some edge locations. Thus, in the above examples, an edge location refers to an extension of at least data plane capacity that is positioned at the edge of the cloud provider network, close to customer devices and/or workloads.