Context. Near-IR polarimetric images of protoplanetary disks enable us to characterize substructures that might be due to the interaction with (forming) planets. The available census is strongly biased toward massive disks around old stars, however. Aims. The DARTTS program aims at alleviating this bias by imaging a large number of T Tauri stars with diverse properties. Methods. DARTTS-S employs VLT/SPHERE to image the polarized scattered light from disks. In parallel, DARTTS-A provides ALMA images of the same targets for a comparison of different dust components. In this work, we present new SPHERE images of 21 circumstellar disks, which is the largest sample released to date. We also recalculated some relevant stellar and disk properties ...