During fusion-based metal additive manufacturing, there is an inherent directionality in heat transfer, which leads to columnar grain growth. This may result in cracking and anisotropic mechanical properties in many alloy systems. Therefore, it is important to study the conditions under which columnar-to-equiaxed transition in grain structure occurs. The grain morphology is determined by several factors such as process conditions, local alloy composition, and number density of nucleating sites. In the present work, a model for simulating columnar-to-equiaxed transition is formulated, considering nucleating site size distribution, rapid solidification and constitutional undercooling in multicomponent alloys. Furthermore, the model is coupled with multicomponent Calphad-based thermodynamic and diffusion mobility descriptions. It is demonstrated that including the above aspects is important in accurately predicting the columnar-to-equiaxed transition by comparing with experimental data for an additively manufactured TiB2-reinforced AlSi10Mg alloy. The framework developed in this work may be used to predict columnar-to-equiaxed transition in additively manufactured technical alloys consisting of multiple elements.