  We investigate how the positive scalar curvature controls the size of a Ricci
limit space when it comes from a sequence of $n$-manifolds with non-negative
Ricci curvature and strictly positive scalar curvature lower bound. We prove
such a limit space can split off $\mathbb{R}^{n-2}$ at most, and when the
maximal splitting happens, the other non-splitting factor has an explicit
uniform diameter upper bound. Besides, we study some other consequences of
having positive scalar curvature for manifolds using Ricci limit spaces
techniques, for instance volume gap estimates and volume growth order
estimates.
