On the number of hyperforests

We consider m-forests with n labeled vertices and T edges. Asymptotic expressions for the number of such hyperforests are obtained as m is fixed and n, T→∞ in such a manner that either 0 < α₀ ≤T/n ≤ α₁ < 1/(m(m-1)), where α₀ and α₁ are some constants, or T/n→1/(m(m−1)) sufficiently fast. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part I, Eger, Hungary, 1994.