  We study transport across a line junction lying between two orthogonal
topological insulator surfaces and a superconductor which can have either
s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. We present a
formalism for studying the effect of a general time-reversal invariant barrier
at the junction and show that such a barrier can be completely described by
three arbitrary parameters. We compute the charge and the spin conductance
across such a junction and study their behaviors as a function of the bias
voltage applied across the junction and the three parameters used to
characterize the barrier. We find that the presence of topological insulators
and a superconductor leads to both Dirac and Schrodinger-like features in
charge and spin conductances. We discuss the effect of bound states on the
superconducting side of the barrier on the conductance; in particular, we show
that for triplet p-wave superconductors such a junction may be used to
determine the spin state of its Cooper pairs. Our study reveals that there is a
non-zero spin conductance for some particular spin states of the triplet Cooper
pairs; this is an effect of the topological insulators which break the spin
rotation symmetry. Finally, we find an unusual satellite peak (in addition to
the usual zero bias peak) in the spin conductance for p-wave symmetry of the
superconductor order parameter.
