We study domain-wall networks on the surface of q-stars in asymptotically
flat or anti de Sitter spacetime. We provide numerical solutions for the whole
phase space of the stable field configurations and find that the mass, radius
and particle number of the star is larger but the scalar field, responsible for
the formation of the soliton, acquires smaller values when a domain-wall
network is entrapped on the star surface.Comment: 11 pages, 6 figures, to appear in Jurn. Math. Phy