  The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech.
P05014 (2012)] is an integrable generalization of the TASEP equipped with an
interaction, which enhances the clustering of particles. The process
interpolates between two extremal cases: the TASEP with parallel update and the
process with all particles irreversibly merging into a single cluster moving as
an isolated particle. We are interested in the large time behavior of this
process on a ring in the whole range of the parameter $\lambda$ controlling the
interaction. We study the stationary state correlations, the cluster size
distribution and the large-time fluctuations of integrated particle current.
When $\lambda$ is finite, we find the usual TASEP-like behavior: The
correlation length is finite; there are only clusters of finite size in the
stationary state and current fluctuations belong to the Kardar-Parisi-Zhang
universality class. When $\lambda$ grows with the system size so does the
correlation length. We find a nontrivial transition regime with clusters of all
sizes on the lattice. We identify a crossover parameter and derive the large
deviation function for particle current, which interpolates between the case
considered by Derrida-Lebowitz and a single particle diffusion.
