The on-lattice ballistic chain-chain aggregation model is studied by Monte Carlo simulations in one, two and three dimensions. The chains move along the lattice directions, with a velocity proportional to kgamma , for a k-mer. The fractal dimension of the large polymers and the mass distribution are computed for different values of the mobility exponent gamma . In two and three dimensions, a long preasymptotic behaviour is observed, and in all dimensions the asymptotic behaviour is in agreement with the Smoluchowski theory.