The existence of blue straggler stars (BSSs) in dwarf spheroidal galaxies (dSphs) is still an open question. In fact, many BSS candidates have been observed in the Local Group dSphs, but it is unclear whether they are real BSSs or young stars. Shedding light on the nature of these BSS candidates is crucial, in order to understand the star formation history of dSphs. In this paper, we consider BSS candidates in Sculptor and Fornax. In Fornax there are strong hints that the BSS population is contaminated by young stars, whereas in Sculptor there is no clear evidence of recent star formation. We derive the radial and luminosity distribution of BSS candidates from wide field imaging data extending beyond the nominal tidal radius of these galaxies. The observations are compared with the radial distribution of BSSs expected from dynamical simulations. In Sculptor the radial distribution of BSS candidates is consistent with that of red horizontal branch (RHB) stars and is in agreement with theoretical expectations for BSSs generated via mass transfer in binaries. On the contrary, in Fornax the radial distribution of BSS candidates is more concentrated than that of all the considered stellar populations. This result supports the hypothesis that most of BSS candidates in Fornax are young stars and is consistent with previous studies.

14 pages, 10 figures, accepted for publication in MNRAS