We show that there are topologically slice links whose individual components are smoothly concordant to the unknot, but which are not smoothly concordant to any link with unknotted components. We also give generalizations in the topological category 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.
"Concordance to links with unknotted components." Algebr. Geom. Topol. 12 (2) 963 - 977, 2012. https://doi.org/10.2140/agt.2012.12.963