  We describe spatio-temporal correlations and heterogeneities in a kinetically
constrained glassy model, the Kob-Andersen model. The kinetic constraints of
the model alone induce the existence of dynamic correlation lengths, that
increase as the density $\rho$ increases, in a way compatible with a
double-exponential law. We characterize in detail the trapping time correlation
length, the cooperativity length, and the distribution of persistent clusters
of particles. This last quantity is related to the typical size of blocked
clusters that slow down the dynamics for a given density.
