**Fundamental principle: a *hierarchical branching network that optimises distribution or collection of something (fluid, information, authority, goods, etc.) with minimal material/effort while maintaining adequate throughput*.**

All of the examples you named are different instantiations of the same abstract pattern:

| Instance | What flows/flows through it | Why it branches |
|----------|----------------------------|-----------------|
| River delta | Water and sediment | Splits the flow into many channels so that the sediment can be deposited progressively and the water can reach a larger area without becoming too shallow. |
| Lightning bolt | Electrical energy | Breaks the high‑potential region into a network of paths, each branch reducing the current density and allowing the discharge to propagate efficiently. |
| Leaf vascular system | Water, nutrients, sugars | Provides a network that spreads resources to every cell in the leaf while keeping the total volume of