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We study the boundaries of relatively hyperbolic HHGs. Using the simplicialstructure on the hierarchically hyperbolic boundary, we characterize bothrelative hyperbolicity and being thick of order 1 among HHGs. In the case ofrelatively hyperbolic HHGs, we show that the Bowditch boundary of the group isthe quotient of the HHS boundary obtained by collapsing the limit sets of theperipheral subgroups to a point. In establishing this, we give a constructionthat allows one to modify an HHG structure by including a collection ofhyperbolically embedded subgroups into the HHG structure.

Relative hyperbolicity, thickness, and the hierarchically hyperbolic boundary