  In this paper, we establish a central limit theorem for a large class of
general supercritical superprocesses with spatially dependent branching
mechanisms satisfying a second moment condition. This central limit theorem
generalizes and unifies all the central limit theorems obtained recently in
Mi{\l}o\'{s} (2012, arXiv:1203:6661) and Ren, Song and Zhang (2013, to appear
in Acta Appl. Math., DOI 10.1007/s10440-013-9837-0) for supercritical super
Ornstein-Uhlenbeck processes. The advantage of this central limit theorem is
that it allows us to characterize the limit Gaussian field. In the case of
supercritical super Ornstein-Uhlenbeck processes with non-spatially dependent
branching mechanisms, our central limit theorem reveals more independent
structures of the limit Gaussian field.
