A pre-polymerized catalyst component for the polymerization of olefins endowed with high activity and morphological stability comprises a non-stereospecific solid catalyst component containing Ti, Mg and a halogen, and an amount of an ethylene/alpha-olefin block (co)polymer ranging from 0.1 up to 5 g per g of said solid catalyst component, said prepolymerized catalyst component being characterized by a mercury porosity, due to pores having radius up to 1 μm, ranging from 0.15 to 0.5 cm3/g and by the fact that at least 55% of said porosity is due to pores having pore radius up to 0.2 μm.