A comprehensive description of the self-assembled formation of GaN nanowires (NWs) by plasma-assisted molecular beam epitaxy (PAMBE) on amorphous-Al x O y buffered Si is presented. The incubation time that precedes the formation of GaN NWs is analyzed as a function of the growth parameters using line-of-sight quadrupole mass spectrometry. We found that the incubation time follows an Arrhenius-type temperature dependence as well as an inverse power law with respect to the Ga flux. Our results reveal a weaker dependence of the incubation time on the Ga flux and faster nucleation on amorphous-Al x O y in comparison to conventional nitridated Si substrates. In addition, an unprecedented analysis of the dependence of the incubation time on the N flux demonstrates a stronger dependence of the incubation time on the N than on the Ga flux. Our results are summarized in growth diagrams to visualize the impact of the growth parameters on the incubation time. The diagrams can also be used to predict the incubation time for so far unexplored growth conditions. Finally, we measured the desorbing Ga flux upon the nucleation stage to determine the growth parameters that result in effective N-rich conditions as required for the self-assembled formation of GaN NWs. These original measurements were combined with the knowledge gained on the incubation time to create a growth map that illustrates the different growth regimes that can be obtained when GaN is grown on an amorphous-Al x O y buffer layer, regardless of the host substrate. Such a map provides a useful guide to induce the growth and control the morphology of GaN NW ensembles on amorphous-Al x O y . Results presented in this work allow to conclude that amorphous-Al x O y is preferred over nitridated Si as it enables shorter incubation times as well as a wider range of growth parameters to induce the self-assembled formation of GaN NWs in PAMBE.