We introduce relative CS-Rickart objects in abelian categories, as common generalizations of relative Rickart objects and extending objects. We study direct summands and (co)products of relative CS-Rickart objects as well as classes all of whose objects are self-CS-Rickart. Corresponding results for dual relative CS-Rickart objects may be automatically obtained by the duality principle. Applications are given to Grothendieck categories and, in particular, to module and comodule categories.