Survival probabilities for N-ary subtrees on a Galton–Watson family tree

The family tree of a Galton–Watson branching process may contain NN-ary subtrees, i.e. subtrees whose vertices have at least N≥1N≥1 children. For family trees without infinite NN-ary subtrees, we study how fast NN-ary subtrees of height tt disappear as t→∞t→∞.