Connected components of Morse boundaries of graphs of groups

Let a finitely generated group G split as a graph of groups. If edge groups are undistorted and do not contribute to the Morse boundary ∂MG, we show that every connected component of ∂MG with at least two points originates from the Morse boundary of a vertex group. Under stronger assumptions on the edge groups (such as wideness in the sense of Dru{t}u-Sapir), we show that Morse boundaries of vertex groups are topologically embedded in ∂MG.