Are participatory platforms facilitating public deliberation? To answer this question, we focus on the most commented citizens' proposal discussed on the Barcelona government's platform Decidim (i.e., the granting of new licenses for tourist apartments). Our goal is twofold. First, we evaluate via content analysis the deliberative quality of this conversation through a carefully selected system of indicators following the classical literature on deliberation. Second, we examine how deliberative quality criteria evolve through interaction, by introducing the dimension of depth, inspired on social computing research. The findings show that the relation between deliberative quality and depth of conversation is mostly curvilinear. The level of justification decreases as conversations go deeper, whereas the levels of reciprocity and incivility become more important over time before decreasing at a later stage. Overall, we conclude that online citizen deliberation can spontaneously emerge, but additional institutional conditions are required to make it last.