  Many galaxy clusters host Mpc scale diffuse radio sources called radio halos.
Their origin is connected to the processes that lead to the formation of
clusters themselves. In order to unveil this connection, statistical studies of
radio halos are necessary. We selected a sample of galaxy clusters with
M500>6e14Msun and z=0.08-0.33 from the Planck SZ catalogue. In paper I, we
presented the radio and X-ray data analysis that we carried out on these
clusters. Here, we study the radio properties of the sample, in connection to
the mass and dynamical state of clusters. We used the dynamical information
derived from the X-ray data to assess the role of mergers in the origin of
radio halos. We studied the distribution of clusters in the radio power-mass
diagram and the role of dynamics on the radio luminosity and emissivity of
radio halos. We measured the occurrence of radio halos as a function of the
cluster mass and we compared it with the expectations of turbulent acceleration
models. We found that more than the 90% of radio halos are in merging clusters
and that their radio power correlates with the mass of the host clusters. The
correlation shows a large dispersion. Interestingly, we showed that cluster
dynamics contributes significantly to this dispersion with more disturbed
clusters being more radio luminous. Clusters without radio halos are generally
relaxed and the upper limits to their diffuse emission lie below the
correlation. We showed that the radio emissivity of clusters exhibits an
apparent bimodality, with the emissivity of radio halos being at least 5 times
larger than the non-emission associated with more relaxed clusters. We found
that the fraction of radio halos drops from ~70% in high mass clusters to ~35%
in the lower mass systems of the sample and we showed that this result is in
good agreement with the expectations from turbulent re-acceleration models.
