A search for transiting planets around FGKM dwarfs and sub-giants in the TESS Full Frame Images of the Southern ecliptic hemisphere

In this work, we present the analysis of 976 814 FGKM dwarf and sub-giant stars in the TESS Full Frame Images (FFIs) of the Southern ecliptic hemisphere. We present a new pipeline, DIAmante, developed to extract optimized, multi-sector photometry from TESS FFIs and a classifier, based on the Random Forest technique, trained to discriminate plausible transiting planetary candidates from common false positives. A new statistical model was developed to provide the probability of correct identification of the source of variability. We restricted the planet search to the stars located in the least crowded regions of the sky and identified 396 transiting planetary candidates among which 252 are new detections. The candidates' radius distribution ranges between 1 R$\rm_{\oplus}$ and 2.6 R$\rm_J$ with median value of 1 R$\rm_J$ and the period distribution ranges between 0.25 days and 105 days with median value of 3.8 days. The sample contains four long period candidates (P>50 days) one of which is new and 64 candidates with periods between 10 and 50 days (42 new ones). In the small planet radius domain (R<4 R$\rm_{\oplus}$) we found 39 candidates among which 15 are new detections. Additionally, we present 15 single transit events (14 new ones), a new candidate multi-planetary system and a novel candidate around a known TOI. By using {\it Gaia} dynamical constraints we found that 70 objects show evidence of binarity. We release a catalog of the objects we analyzed and the corresponding lightcurves and diagnostic figures through the MAST and ExoFOP portals.