We present a streaming framework for seamless building reconstruction from huge aerial LiDAR point sets. By storing data as stream files on hard disk and using main memory as only a temporary storage for ongoing computation, we achieve efficient out-of-core data management. This gives us the ability to handle data sets with hundreds of millions of points in a uniform manner. By adapting a building modeling pipeline into our streaming framework, we create the whole urban model of Atlanta from 17.7GB LiDAR data with 683M points in under 25 hours using less than 1GB memory. To integrate this complex modeling pipeline with our streaming framework, we develop a state propagation mechanism, and extend current reconstruction algorithms to handle the large scale of data.