  We show that there are links whose individual components are concordant to
the unknot, but which are not concordant to any link with unknotted components.
We give examples in the topological category, and examples in the smooth
category which are topologically slice. We also give generalizations regarding
components of prescribed Alexander polynomials. The main tools are covering
link calculus, algebraic invariants of rational knot concordance theory, and
the correction term of Heegaard Floer homology.
