We develop a simple model of planetary formation, focusing our attention on those planets with masses less than 10 M⊕ and studying particularly the primordial spin parameters of planets resulting from the accretion of planetesimals and produced by the collisions between the embryos. As initial conditions, we adopt the oligarchic growth regime of protoplanets in a disc where several embryos are allowed to form. We take different initial planetary system parameters and for each initial condition, we consider an evolution of 2 × 107 yr of the system. We perform simulations for 1000 different discs, and from their results we derive the statistical properties of the assembled planets. We have taken special attention to the planetary obliquities and rotation periods, such as the information obtained from the mass and semimajor axis diagram, which reflects the process of planetary formation. The distribution of obliquities was found to be isotropic, which means that planets can rotate in direct or indirect sense, regardless of their mass. Our results regarding the primordial rotation periods show that they are dependent on the region where the embryo was formed and evolved. According to our results, most of the planets have rotation periods between 10 and 10 000 h and there are also a large population of planets similar to terrestrial planets in the Solar system.