Star-shaped donor-acceptor molecules are full of promise for organic photovoltaics and electronics. However, the effect of the branching core on physicochemical properties, charge transport and photovoltaic performance of such donor-acceptor materials in single-component (SC) and bulk heterojunction (BHJ) organic solar cells has not been thoroughly addressed. This work shows the comprehensive investigation of six star-shaped donor-acceptor molecules with terminal hexyldicyanovinyl blocks linked through 2,2′-bithiophene π-conjugated bridge to different electron-donating cores such as the pristine and fused triphenylamine, tris(2-methoxyphenyl)amine, carbazole- and benzotriindole-based units. Variation of the branching core strongly impacts on such important properties as the solubility, highest occupied molecular orbital energy, optical absorption, phase behavior, molecular packing and also on the charge-carrier mobility. The performance of SC or BHJ organic solar cells are comprehensively studied and compared. The results obtained provide insight on how to predict and fine-tune photovoltaic performance as well as properties of donor-acceptor star-shaped molecules for organic solar cells.