# On the maximal offspring in a subcritical branching process

## TL;DR

This paper investigates the behavior of the maximum number of offspring in a large subcritical Galton--Watson tree conditioned on size, providing asymptotic limits under certain regularity conditions.

## Contribution

It establishes new asymptotic results for the maximal offspring in conditioned subcritical Galton--Watson trees, extending understanding of their structural properties.

## Key findings

- Limits for the maximal offspring as tree size grows
- Asymptotic distribution results under regularity assumptions
- Insights into the structure of conditioned subcritical Galton--Watson trees

## Abstract

We consider a subcritical Galton--Watson tree conditioned on having $n$ vertices with outdegree in a fixed set $\Omega$. Under mild regularity assumptions we prove various limits related to the maximal offspring of a vertex as $n$ tends to infinity.