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 three-dimensional (3D) Bernevig-Hughes-Zhang model and compare the results with those from an effective two-dimensional (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 us to model systems of micron size, typical of experimental setups but computationally too heavy for 3D models.