[en] The properties of Ξ${}^{-<!--\; ???\; -->}$ hypernuclei are studied systematically using a two-dimensional Skyrme-Hartree-Fock approach combined with three different ΞN Skyrme forces fitted to reproduce the existing data. We explore the impurity effect of a single Ξ${}^{-<!--\; ???\; -->}$ hyperon on the radii, deformations, and density distributions of the nuclear core and point out qualitative differences between the different forces. We find that the Ξ${}^{-<!--\; ???\; -->}$ removal energy of ${}_{\mathrm{\Xi <!--\; ??\; -->}p}^{13}$B [${}^{12}$C(g.s.)+Ξ${}^{-<!--\; ???\; -->}$(1p)] calculated by the SLX3 force is 0.7 MeV, which is in good agreement with a possible value of 0.82±0.17MeV from the KEK E176 experiment. The theoretical prediction for this weakly bound state depends strongly on the deformation of the nuclear core, which is analyzed in detail.