We numerically study crossed Andreev reflection (CAR) in a topological insulator nanowire T-junction where one lead is proximitized by a superconductor. We perform realistic simulations based on the 3D BHZ model and compare the results with those from an effective 2D surface model, whose computational cost is much lower. Both approaches show that CAR should be clearly observable in a wide parameter range, including perfect CAR in a somewhat more restricted range. Furthermore,it can be controlled by a magnetic field and is robust to disorder. Our effective 2D implementation allows to model systems of micronsize, typical of experimental setups, but computationally too heavy for 3D models.