Abstract: The electronic band alignment in semiconductor heterostructures is a key factor for their use in electronic applications. The alignment problem has been intensively studied for bulk systems but is less well understood for low-dimensional heterostructures. In this work we investigate the alignment in two-dimensional lateral heterostructures. First-principles calculations are used to show that the electronic band offset depends crucially on the width and thickness of the heterostructure slab. The particular heterostructures under study consist of thin hydrogenated and fluorinated diamond slabs which are laterally joined together. Two different limits for the band offset are observed. For infinitely wide heterostructures the vacuum potential above the two materials is aligned leading to a large step potential within the heterostructure. For infinitely thick heterostructure slabs, on the other hand, there is no potential step in the heterostructure bulk, but a large potential step in the vacuum region above the heterojunction is observed. The band alignment in finite systems depends on the particular dimensions of the system. These observations are shown to result from an interface dipole at the heterojunction that tends to align the band structures.