Which authority has the responsibility for integrating all emergency medical services systems in California?

The Emergency Medical Services Authority (EMSA) is the correct choice because it is specifically tasked with overseeing and coordinating the delivery of emergency medical services in California. This includes integrating the various components of emergency medical services (EMS) systems across the state, ensuring that they function in a cohesive and efficient manner to provide high-quality care to patients during emergencies. The EMSA's role encompasses developing policies, regulations, and standards that govern EMS practices and operations, thereby ensuring consistency and excellence in emergency medical care.

Other entities, such as the Department of Health Services and the California Medical Board, have important roles in public health and the regulation of medical professionals, respectively, but they do not have the primary responsibility for the integration of the state's EMS systems. The State Emergency Office, while it may be involved in wider emergency management activities, is not specifically focused on the EMS integration.