A copolymer of ethylene and an alpha-olefin contains from 3 to 12 carbon atoms, wherein 0.1 to 1.5 mol % of the units originate from the alpha-olefin. The copolymer has a relative density ranging from 0.960 to 0.940, a transition metal content lower than 6 ppm, an Mw/Mn ratio higher than 7, an Mz/Mw ratio higher than 3.3 and an Mz higher than 300,000. The copolymer is prepared from the polymerization or co-polymerization of at least one olefin in the presence of a solid catalytic component or a prepolymerized catalyst.