To gain insight into divertor operation, similarity techniques are employed to investigate whether model systems of equations plus boundary conditions admit scaling transformations that lead to useful divertor scaling laws. These can be used to perform similarity experiments or more fully exploit large computer simulations. Fluid plasma models of the divertor region are adopted that ignore anomalous processes. We consider neutral descriptions in both the short and long mean-free path limits. As usual, the more approximations that are made, the more scaling transformations are allowed, leading to fewer independent dimensionless parameters that need to be considered, thereby imposing fewer divertor similarity constraints. The simplest model considered balances electron heat conduction with impurity radiation and places the fewest constraints on similarity. To be able to model the onset of detached divertor operation in short mean-free path regimes, a fluid neutral description is employed that balances plasma pressure by neutral pressure. In this model the constraints on divertor similarity are most severe. A less constrained long mean-free path or Knudsen neutral model is also considered. It models the onset of detached divertor operation by balancing plasma pressure by momentum transfer to the neutrals that are randomized by collisions with the deep slot sidewalls. The simpler models have relaxed divertor similarity constraints, but all models remain severely restricted by the collisionality constraints.