Recent observations show that inner discs and rings (IDs and IRs) are not preferentially found in barred galaxies, pointing to the relevance of formation mechanisms different to the traditional bar-origin scenario. Nevertheless, the role of minor mergers in the formation of these inner components (ICs), while often invoked, is still poorly understood. We have investigated the capability of minor mergers to trigger the formation of IDs and IRs in spiral galaxies through collisionless N-body simulations. All the simulated minor mergers develop thin rotationally-supported ICs out of satellite material. A wide morphological zoo of ICs has been obtained (including IDs, IRs, pseudo-rings, nested IDs, nuclear bars, and combinations of them), all with structural and kinematical properties similar to observations. Their existence can be deduced through the features that they imprint in the isophotal profiles and kinemetric maps of the final remnant, as in many real galaxies. The present models prove that minor mergers are an efficient mechanism to form rotationally-supported stellar ICs in spiral galaxies, neither requiring strong dissipation nor noticeable bars, and suggest that their role in the formation of ICs must have been much more complex than just bar triggering.