  Recently Ren et al. [Stoch. Proc. Appl., 137 (2021)] have proved that the
extremal process of the super-Brownian motion converges in distribution in the
limit of large times. Their techniques rely heavily on the study of the
convergence of solutions to the Kolmogorov-Petrovsky-Piscounov equation along
the lines of [M. Bramson, Mem. Amer. Math. Soc., 44 (1983)]. In this paper we
take a different approach. Our approach is based on the skeleton decomposition
of super-Brownian motion. The skeleton may be interpreted as immortal particles
that determine the large time behaviour of the process. We exploit this fact
and carry asymptotic properties from the skeleton over to the super-Brownian
motion. Some new results concerning the probabilistic representations of the
limiting process are obtained, which cannot be directly obtained through the
results of [Y.-X. Ren et al., Stoch. Proc. Appl., 137 (2021)]. Apart from the
results, our approach offers insights into the driving force behind the
limiting process for super-Brownian motions.
