We present here detailed results on multifractality based on Hwa's formalism in proton - nucleus interactions at an energy of 800 GeV. The dependence on the target and the number of collisions in an interaction, on the multifractal characteristics has been analysed in terms of moments in a two-dimensional phase space. The power-law behaviour of the moments suggests a multifractal behaviour. The spectrum of the rapidity density index has been determined for nucleon and AgBr targets and also for the different number of collisions in the interactions, which exhibits self-similarity. The rescaled spectrum has also been investigated for various classes of interactions. The distributions show the universality of the multifractal structure for q>1.