  In this paper, we first establish a decomposition theorem for size-biased
Poisson random measures. As consequences of this decomposition theorem, we get
a spine decomposition theorem and a 2-spine decomposition theorem for some
critical superprocesses. Then we use these spine decomposition theorems to give
probabilistic proofs of the asymptotic behavior of the survival probability and
Yaglom's exponential limit law for critical superprocesses.
