phase of the Vicsek model was already noticed in [@Huepe2004; @Chate2008], where a power $\alpha\lesssim 2$ was observed in the homogeneous polarized state, while $\alpha\gtrsim2$ closer to the onset of flocking where dense traveling bands are in coexistence with an incoherent background. A similar behavior was also reported for non-aligning self-propelled hard disks in [@Levis2014], with a universal power $\alpha\approx 1.7$ associated with a percolation transition; and for self-propelled hard rods in [@Peruani2006], also displaying a structural phase transition indicating the emergence of a macroscopic structure. In our model, we find an exponent $\alpha\approx 2$ which weakly depends on the distance to the transition point.

![Cluster-size distribution $c_n$ for $\text{Pe}=333.3$ and several $\text{g}$. As $\text{g}$ is increased the distribution changes from an exponential decay to an algebraic $1/n^2$ decay for $\text{g}\approx2.25$. At higher $\text{g}>\text{g}^*\approx2.25$, exponential with a big bump indicating a big cluster. Just in the transition we can appreciate how the $1/n^2$ decay fits the data points.[]{data-label="fig:CDF"}](CDF.pdf)

We turn now into the description of the dense structures found in the MC regime. Phenomenologically, the recurrence of finding large elongated polarized structures is higher for larger $\text{g}$. Strikingly though, at a given value of $\text{g}$, band and lane structures can 