  Given an integer k, we consider the parallel k-stripping process applied to a
hypergraph H: removing all vertices with degree less than k in each iteration
until reaching the k-core of H. Take H as H_r(n,m): a random r-uniform
hypergraph on n vertices and m hyperedges with the uniform distribution. Fixing
k,r\ge 2 with (k,r)\neq (2,2), it has previously been proved that there is a
constant c_{r,k} such that for all m=cn with constant c\neq c_{r,k}, with high
probability, the parallel k-stripping process takes O(\log n) iterations. In
this paper we investigate the critical case when c=c_{r,k}+o(1). We show that
the number of iterations that the process takes can go up to some power of n,
as long as c approaches c_{r,k} sufficiently fast. A second result we show
involves the depth of a non-k-core vertex v: the minimum number of steps
required to delete v from H_r(n,m) where in each step one vertex with degree
less than k is removed. We will prove lower and upper bounds on the maximum
depth over all non-k-core vertices.
