  We study the relaxation of the local ferromagnetic order in the transverse
field quantum Ising chain with power-law decaying interactions $1/r^{\alpha}$.
We prepare the system in the GHZ state and study the time evolution of the
probability distribution function (PDF) of the order-parameter within a block
of $l$ when quenching the transverse field. The model is known to support
long-range order at finite temperature for $\alpha \leq 2.0$ . In this regime,
quasi-localized topological magnetic defects are expected to strongly affect
the equilibration of the full probability distribution. We highlight different
dynamical regimes where gaussification mechanism may be slowed down by
confinement and eventually breaks. We further study the PDF dynamics induced by
changing the effective dimensionality of the system; we mimic this by quenching
the range of the interactions. As a matter of fact, the behavior of the system
crucially depends on the value of $\alpha$ governing the unitary evolution.
