Loose octree
An octree variant whose node boxes are enlarged so that an object straddling a boundary still fits inside a single node.
A plain octree has an annoying problem: an object lying across a split plane must either be stored high up the tree or divided among several nodes. A loose octree solves this by "loosening" each node's bounds — typically doubling the side length — so they overlap their neighbours. An object is then placed in the node its centre falls into, and fits whole no matter where it happens to sit.
Thatcher Ulrich described the trick in Game Programming Gems (2000). The price is that every query must test slightly larger boxes, but insertion and update are simple and cheap — ideal for moving objects, where a strict tree would constantly need rebuilding.