Let X be an irreducible smooth projective curve, of genus at least two, over an algebraically closed field k. Let $mathcal{M}^d_G$ denote the moduli stack of principal G-bundles over X of fixed topological type $d in pi_1(G)$, where G is any almost s
imple affine algebraic group over k. We prove that the universal bundle over $X times mathcal{M}^d_G$ is stable with respect to any polarization on $X times mathcal{M}^d_G$. A similar result is proved for the Poincare adjoint bundle over $X times M_G^{d, rs}$, where $M_G^{d, rs}$ is the coarse moduli space of regularly stable principal G-bundles over X of fixed topological type d.
Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has ADE-singularities. Let G be the reductive group given by the root system of these singularities. We construct
a G-torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of Friedman and Morgan for individual singular del Pezzo surfaces. In case of very good residue characteristic, this torsor is unique and infinitesimally rigid.
