A comprehensive, transient three-dimensional model of a single-pass laser surface alloying process has been developed and used to examine the heat, momentum and species transport phenomena. A numerical study is performed in a co-ordinate system moving with the laser at a constant scanning speed. In this model a fixed grid enthalpy-porosity approach is used, which predicts the evolutionary pool development. In this model two extreme cases of alloying element and base metal combinations are considered based on their relative melting points. One extreme case is for an alloying element with its melting point much lower than that of the base metal. In this case the alloying element melts almost instantaneously. Hence it is assumed that the alloying element introduced on the melt pool surface is in the molten state. Thus, while solving the species conservation equation a species flux condition is used on the entire melt pool surface. This case is analysed for aluminium alloying element on iron base metal. The final species distribution in the melt pool as well as in the solidified alloy is predicted. The other extreme case is studied for an alloying element with its melting point relatively higher than that of the base metal. In this case all the alloying element particles on the melt pool surface will not melt. Only those particles which fall in the region on the melt pool surface where the local temperature is higher than the melting point of the alloying element will melt. The particles which fall away from this region are advected into the melt pool, due to a strong Marangoni convection on the melt pool surface. If a particle is advected into the inner region in the melt pool (where the temperature is higher than its melting point), it starts melting and thus the molten species mass gets distributed. Hence, the species flux condition at the entire surface of the melt pool is not valid. The particles are tracked in the melt pool by assuming the alloying particles to be spherical in shape and moving without any relative velocity with the surrounding fluid. Simultaneously, the temperature field inside the spherical particle is solved by assuming its surface temperature to be the local temperature in the melt pool. The amount of particle mass that fuses as it passes through a particular control volume is noted. The same procedure is repeated for a large number of particles initiated at various locations on the pool surface, and a statistical distribution of the species mass source in the entire pool is obtained. This species mass source distribution is then used to solve the species conservation equation. Nickel alloying element on aluminium base metal is used to illustrate this case. The numerical results obtained from the two cases are compared with the available experimental results. A qualitative matching is found between the numerical and experimental results.