Important metallurgical factors, such as alloying aluminum redistribution, supersaturation and undercooling of dendrite tip around solid/liquid interface, are separately optimized to alleviate stray grain formation and columnar/equiaxed transition (CET) with series of welding conditions and provide a very efficient method for microstructure control through modification of growth kinetics of dendrite tip under nonequilibrium solidification conditions of ternary Ni-Cr-Al molten pool. Asymmetrical (001)/[110] welding configuration is inferior to symmetrical (001)/[100] welding configuration, because overall area-weighted alloying redistribution, supersaturation and undercooling of dendrite tip throughout the solid/liquid interface of weld pool are consistently severer to exacerbate solidification behavior and microstructure development and incur morphology instability of columnar/equiaxed transition. High heat input, such as combination of higher laser power and slower welding speed, monotonically increases aluminum enrichment, supersaturation and undercooling of dendrite tip near solidification interface to simultaneously deteriorate nucleation and growth of stray grain formation and weaken columnar dendrite morphology, while low heat input, such as combination of lower laser power and faster welding speed, decreases solute buildup, relieves supersaturation and beneficially suppresses dendrite tip undercooling to minimize equiaxed dendrite morphology in the crack-susceptible region, and thereby facilitate single-crystal epitaxial growth with decrease of thermo-metallurgical factors for columnar/equiaxed transition in order to provide prerequisite for optimization of welding conditions. Favorable solidification conditions are obtainable with preferential crystallographic orientation to eliminate columnar/equiaxed transition under which the epitaxy of single-crystal metallurgical properties across fusion boundary of substrate is predominantly promoted to essentially reduce stray grain formation in (001)/[100] welding configuration, and is kinetically capable of significant reduction of microstructure anomalies and nonuniform solidification behavior. The useful relationship among welding conditions, alloying aluminum redistribution, supersaturation and undercooling of dendrite tip is properly established within dendrite stability range through thorough analysis. In addition, the validation of theoretical predictions is fairly reasonable by the experiment results. It is worth that the contributions of kinetics-related solidification phenomena with advancement of solid/liquid interface are imposed altogether to understand why stray grain formation occurs on the basis of controlling mechanism of minimum undercooling or minimum velocity by the reproducible methodology procedure.