geo/Connectivity

Two primitives belong to the same piece when they share a point, directly or through a chain of other primitives. Everything that hangs together comes out as one object, everything that does not comes out as its own, and nothing else changes. Use it to pull a merged curve back apart, to count the islands in a cut, or to give each piece its own transform downstream.

Connection is by shared POINT, so two faces meeting at a single corner are one piece. A fork stays whole too: a T junction of three segments is one object, not three arms. If you want the arms, that is a different question and a different tool.

NO primitive in Polygon welds its points: each face carries its own corners, so a raw geo/Box splits into SIX objects, one per face, and a geo/Sphere into one per quad, even though both look solid. That is the geometry as stored, not a bug in the split. Put a geo/Fuse in front to weld the corners and the box comes back as a single object. geo/ManifoldDisplay reports the same fact from the other side, as 24 open edges on that box.

It takes segments, triangles, quads, hexagons and tetrahedra. A curve or a solid whose points live outside the buffers, a NURBS or a CAD shape, has to be converted first: geo/CADTriangulate for CAD, geo/VolumeTriangulate for a volume. A point cloud is refused outright, because every point in it is its own piece and the answer would be one object per point.