The present work deals with the evaluation of gas boundary layer characteristics under conditions of a high-pressurized gas flow through narrow kerfs as prevalent in laser fusion cutting. A simplistic two-dimensional channel model with appropriate boundary conditions in combination with empirical correlations of the similitude theory is applied to determine the flow state and the thickness of the boundary layer as well as magnitudes of momentum and heat transfer rates. The estimations show that the most expectable flow state of the boundary layer corresponds to a transitional regime. Calculated boundary layer thicknesses lie in a range of 100 to 300 microns after a considered running length of 10 mm. Thus, the formation of the characteristic cut edge topography with typical maximum roughness values for Rz of about 50 microns for high-quality solid-state laser fusion cuts will take place within the boundary layer region. It can be concluded, that the knowledge of the particular spatial and temporal flow structure of the boundary layer should be considered of being indispensable for a profound understanding of the formation mechanisms of the cut edge topography.