English: In old dense stellar systems collisions of white dwarfs are a rather frequent phenomenon. Here we present the results of several Smoothed Particle Hydrodynamics simulations of close encounters of white dwarfs to explore under which conditions collisions occur and which are the final remnants of the interaction. Depending on the initial conditions, three different outcomes are possible. Specifically, the outcome of the interaction can be either a direct or a lateral collision or the interaction can result in the formation of an eccentric binary system. The large number of simulations performed has allowed us to identify the key parameters to parametrize the outcome of the interaction as a function of the initial conditions. We find that the outcome of the interaction mostly depends on the periastron distance and the reduced mass of the system. Finally, we discuss the influence of the masses and chemical compositions of the interacting white dwarfs in the properties of the remnants.