Polygons with holes must be handled in digital cartography, 2D and 3D modelling, image analysis and picture generation. The Dissassociative Area Model (DAM) described in this paper uses polygonal units of uncut space, termed primitive regions, in the representation of the geometric and topoiogical properties of a set of areal entities. Algorithms and a data structure are presented which extract boundaries of these polygons from vector data and determine their topology. The algorithms recognise the containment hierarchy of polygons with holes without the need for information relating to the areal entities. The hierarchy is represented by a rooted tree of boundaries, rather than regions, and does not involve bridges between inner and outer boundaries.