2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128363A quenched central limit theorem is derived for the super-Brownian motion with super-Brownian immigration, in dimension $d\geq 4$. At the critical dimension $d=4$, the quenched and annealed fluctuations are of the same order but are not equal.A small mistake in the proof of Proposition 2.2 is corrected, and typos removedProbability60J80; 60F05text