We present an efficient approach for end-to-end out-of-core construction and interactive inspection of very large arbitrary surface models. The method tightly integrates visibility culling and out-of-core data management with a level-of-detail framework. At preprocessing time, we generate a coarse volume hierarchy by binary space partitioning the input triangle soup. Leaf nodes partition the original data into chunks of a fixed maximum number of triangles, while inner nodes are discretized into a fixed number of cubical voxels. Each voxel contains a compact direction dependent approximation of the appearance of the associated volumetric subpart of the model when viewed from a distance. The approximation is constructed by a visibility aware algorithm that fits parametric shaders to samples obtained by casting rays against the full resolution dataset. At rendering time, the volumetric structure, maintained off-core, is refined and rendered in front-to-back order, exploiting vertex programs for GPU evaluation of view-dependent voxel representations, hardware occlusion queries for culling occluded subtrees, and asynchronous I/O for detecting and avoiding data access latencies. Since the granularity of the multiresolution structure is coarse, data management, traversal and occlusion culling cost is amortized over many graphics primitives. The efficiency and generality of the approach is demonstrated with the interactive rendering of extremely complex heterogeneous surface models on current commodity graphics platforms.