Galton-Watson random forests with a given number of root trees and a known number of nonroot vertices are investigated. The distribution of the number of direct offspring of each particle in the forest- generating process is assumed to have infinite variance. Branching processes of this kind are used successfully to study configuration graphs aimed at simulating the structure and development dynamics of complex communication networks, in particular the internet. The known relationship between configuration graphs and random forests reflects the local tree structure of simulated networks. Limit theorems are proved for the maximum size of a tree in a random forest in all basic zones where the number of trees and the number of vertices tend to infinity.

Bibliography: 14 titles.

研究了具有给定根树数量和已知数量的非根顶点的 Galton-Watson 随机森林。假设森林生成过程中每个粒子的直接后代数量分布具有无限方差。这种分支过程成功地用于研究旨在模拟复杂通信网络，尤其是互联网的结构和发展动态的配置图。配置图和随机森林之间的已知关系反映了模拟网络的局部树结构。在所有基本区域中树的数量和顶点的数量趋于无穷大的随机森林中，证明了树的最大尺寸的极限定理。

参考书目：14个标题。