  We investigate the concordance properties of `parallel links' P(K), given by
the (2,0) cable of a knot K. We focus on the question: if P(K) is concordant to
a split link, is K necessarily slice? We show that if P(K) is smoothly
concordant to a split link, then many smooth concordance invariants of K must
vanish, including the tau and s-invariants, and suitably normalized
d-invariants of surgeries on K. We also investigate the (2,2m) cables P_m(K),
and find obstructions to smooth concordance to the sum of the (2,2m) torus link
and a split link.
