  We consider a critical superprocess $\{X;\mathbf P_\mu\}$ with general
spatial motion and spatially dependent stable branching mechanism with lowest
stable index $\gamma_0 > 1$. We first show that, under some conditions,
$\mathbf P_{\mu}(\|X_t\|\neq 0)$ converges to $0$ as $t\to \infty$ and is
regularly varying with index $(\gamma_0-1)^{-1}$. Then we show that, for a
large class of non-negative testing functions $f$, the distribution of
$\{X_t(f);\mathbf P_\mu(\cdot|\|X_t\|\neq 0)\}$, after appropriate rescaling,
converges weakly to a positive random variable $\mathbf z^{(\gamma_0-1)}$ with
Laplace transform $E[e^{-u\mathbf
z^{(\gamma_0-1)}}]=1-(1+u^{-(\gamma_0-1)})^{-1/(\gamma_0-1)}.$
