a phase transition from an isotropic state of zero polarization, to an ordered state characterized by the collective motion of the system, which acquires a net polarization, $P>0$, and the presence strong density heterogeneities. The alignment interaction polarizes the clusters and promotes the formation of structures whose size increases with $\text{g}$, eventually leading to a (macroscopic) large high density structure (see the snapshots Fig.\[fig:PhD\] (d-f)).

Indeed, for a given $\text{Pe}$, there is a critical alignment $\text{g}^*$ above which a macroscopic polar cluster appears (hence called MC phase) . The location $\text{g}^*$ is indicated by green symbols in the phase diagram Fig.\[fig:PhD\] (a). Instead, in the intermediate region between the flocking threshold and the emergence of a macroscopic structure, $\text{g}^c<\text{g}<\text{g}^*$, the system sets in a state made of a distribution of coherently moving finite-size ‘microscopic’ polar clusters (hence called mC phase). As shown in Fig. \[fig:CDF\], as we increase $\text{g}$ at fixed $\text{Pe}$ the cluster size distribution broadens and a transition towards a state characterized by the appearance of a ‘macroscopic’ cluster (MC) is observed at $\text{g}^*$.

In the low persistence regime $\text{Pe}\lesssim 1$ the advent of a macroscopic polar structure is controlled by the establishment of polar order in the 