Epitaxial Laser Metal Forming (E-LMF) consists in impinging a jet of metallic powder onto a molten pool formed by controlled laser heating and thereby, generating epitaxially a single crystal deposit onto a single crystal substrate. It is a near net-shape process for rapid prototyping or repair engineering of single crystal high pressure/high temperature gas turbines blades. Single crystal repair using E-LMF requires controlled solidification conditions in order to prevent the nucleation and growth of crystals ahead of the columnar dendritic front, i.e., to ensure epitaxial growth and to avoid the columnar to equiaxed transition. A major limitation to the process lies in the formation of stray grains which can originate either from heterogeneous nucleation ahead of the solidification front or from remelting of dendrite arms due to local solute enriched liquid flow, .i.e fragmentation. To study this last aspect, heat and fluid flow modelling is required to establish the relationship between process parameters such as laser power, beam diameter and scanning speed, and the local solidification conditions plus the fluid flow in the vicinity of the mushy zone. Surface tension driven convection known as the Marangoni effect needs to be included in the model owing to its large influence on the development of eddies and on the shape of the liquid pool. The 3D model implemented in the FE software calcosoft® is used to compute the fluid convection within the liquid pool and to assess the risk of fragmentation using a criterion based on the local velocity field and thermal gradient. The computed results are compared with EBSD maps of laser traces carried out at EPF-Lausanne in re-melting experiments.