With the increasing ubiquity and scale of self-adaptive systems, there is a growing need to decentralize the functionality that realizes self-adaptation. Our focus is on architecture-based self-adaptive systems where one or more functions for monitoring, analyzing, planning, and executing are realized by multiple components that coordinate with one another. While some earlier studies have shed light on existing work on the decentralization of self-adaptive systems, there is currently no clear overview of the state of the art in decentralization of self-adaptive systems. Yet, having a precise view on the state of the art in decentralized self-adaptive systems is crucial for researchers to understand existing solutions and drive future research efforts. To address this gap, we conducted a mapping study. The study focused on papers published at 24 important venues that publish research on self-adaptation. The study focused on the motivations for choosing a decentralized approach to realize self-adaptation, the adaptation functions that are decentralized, the realization of the coordination, and the open challenges in the area.