  We study the boundaries of relatively hyperbolic HHGs. Using the simplicial
structure on the hierarchically hyperbolic boundary, we characterize both
relative hyperbolicity and being thick of order 1 among HHGs. In the case of
relatively hyperbolic HHGs, we show that the Bowditch boundary of the group is
the quotient of the HHS boundary obtained by collapsing the limit sets of the
peripheral subgroups to a point. In establishing this, we give a construction
that allows one to modify an HHG structure by including a collection of
hyperbolically embedded subgroups into the HHG structure.
