Laser glass deposition is an additive manufacturing method to produce individualized glass components. This process uses a CO2 laser with a defocused beam as a heat source to additively melt-fused silica filaments. The fiber filament is fed laterally in the process zone and is deposited layer-by-layer to form 3D structures. The formation of boundary layers in conventional 3D-printing methods is a usual byproduct of the process. In this paper, the boundary layer formation of deposited fused silica filaments is investigated in detail by means of varying different process parameters such as, laser power, feed rate, laser spot diameter, and printing strategy. This involves examining both thin-walled and thick-walled test specimens. Quality characteristics like the surface roughness and the optical transmission are analyzed for the printed specimen. Finally, fully transparent structures with surface roughness below 100 nm and a transparency of 90\% could be printed boundary layer-free and without post-processing.