We introduce Broadcast by Balanced Saturation (BBS), a general class of tree-based pipelined broadcast algorithms that optimizes communication efficiency across diverse network topologies, with a particular emphasis on large message sizes. By addressing spanning tree construction and communication task scheduling, two fundamental theoretical challenges in broadcasting, BBS offers a unified and flexible framework that operates effectively under varied network constraints. The algorithm maximizes aggregated throughput while simultaneously addressing topology constraints, synchronization overhead, bandwidth limitations and contention. Using SimGrid under standard assumptions, including full-duplex and one-port communication, various algorithms were evaluated on Mesh, Butterfly, Dragonfly, and Fat-Tree topologies. Results demonstrate that BBS consistently outperforms both general-purpose and topology-aware broadcast algorithms across a wide range of topologies and message sizes, establishing it as a robust and high-performance solution for large-scale systems.