The unique solidification kinetics of laser powder bed fusion (LPBF) additive manufacturing tend to result in solidification modes deviating from the phase diagram predictions. This study documents an approach for developing LPBF solidification mode selection process map based on an analytical equation model which determines the solidification mode transition criteria as a function of laser power ( P ), scan velocity ( V ) and material properties. As case studies, solidification mode selection process maps were developed for three Ti6Al4V-xB alloys (x = 1, 2, 5 wt% B), presenting primary β , primary TiB, and coupled eutectic solidification modes. To validate the proposed approach, laser deposition experiments were conducted to fabricate single-tracks, single-layer and two-layer pads on arc-melted Ti6Al4V-xB alloy buttons with different P-V parameters. The model-developed process maps agreed with the experimental results. P-V windows were found to allow coupled-eutectic solidification for off-eutectic Ti6Al4V-1, 2, 5 % B and primary- β solidification for hyper-eutectic Ti6Al4V-5 %B, producing a microstructure with a continuous TiB network and a microstructure with a discontinuous network of nano-scale TiB whiskers respectively. Single-layer and two-layer pads showed consistent microstructure features of the tracks, except for the narrow region that was remelted during pad deposition. Melt pool hardness was measured, which increases with scan velocity and shows a sudden change when solidification mode was altered. The potential and limitations of the proposed method for LPBF microstructure investigation are discussed. • An approach based on analytical models was used to develop a solidification mode selection process map for LPBF. • Solidification process maps were constructed for LPBF of Ti6Al4V-1, 2, 5%B, showing windows for coupled eutectic mode. • By varying P-V parameters, high-B% Ti6Al4V-xB solidification alters from primary TiB to eutectic to primary β-Ti mode. • LPBF with Ti6Al4V-xB could render four TiB morphologies after solidification