A comprehensive theoretical study of the potential energy surfaces of the lowest-lying doublet and quartet electronic states of the SC3H4+ system has been performed by means of a combination of density functional and ab intio methods. The potential energy surfaces corresponding to the lowest doublet and quartet electronic states have turned out to be extremely complex. Twenty-six doublet species and twenty-four quartet species have been identified, some of them having several stable conformations. The quartet states are normally much higher in energy than the doublet states. The absolute minimum is the methylthioketene cation, but the 2H-thiete cation, the thioacrolein cation, and the methylthiirene cation lie very close in energy; all of them are doublet states. The most stable quartet species is the thioxyallyl cation. In addition, a rather detailed analysis of the fragmentation of this system has been made. All of the products that are obtained in the S+ + CH3CCH reaction, which is an important step in the generation of sulfur-containing cumulenes of astrophysical significance, have been included in this analysis, namely, a number of states of the SC3H3+, HCS+, C3H3+, C2H3, and C3H4+ systems. Special attention has been paid to the SC3H3+ system. In addition, the interaction between S+ and CH3CCH through a number of electronic states has been studied by means of a multireference configuration interaction approach. The results suggest that an intersystem crossing process leading to the doublet potential energy surface of the SC3H4+ system may play a key role. Some potentially crucial reaction mechanisms have been proposed.