Branched architectures such as neurons and vascular networks must optimise spatial coverage to perform essential functions. Yet the physical rules driving this self-organised coverage remain poorly understood. In this talk, I will first present theoretical work on how local feedback and global guidance cues shape individual branched structures. I will then address how populations of branching cells collectively partition a shared territory without gaps or redundant overlap. I will show that coupling cell growth to neighbour repulsion yields efficient tiling and progressively suppresses large-scale density fluctuations, driving the system towards a hyperuniform state. Experiments on microglial patterning in the developing retina corroborate these predictions. A coarse-grained description further reveals an optimal regime in the growth-repulsion plane that maximises both tiling efficiency and large-scale regularity. These findings show that efficient space-filling and long-range order can emerge from a single dynamical mechanism, suggesting a general principle for self-organised tissue patterning.