2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66047We describe a method of adding tails to C*-correspondences which generalizes the process used in the study of graph C*-algebras. We show how this technique can be used to extend results for augmented Cuntz-Pimsner algebras to C*-algebras associated to general C*-correspondences, and as an application we prove a gauge-invariant uniqueness theorem for these algebras. We also define a notion of relative graph C*-algebras and show that properties of these C*-algebras can provide insight and motivation for results about relative Cuntz-Pimsner algebras.24 pages, uses XY-pic. A few typos corrected, final version for publicationOperator Algebras46L08, 46L55text