The area of application of the Hall effect thrusters is constantly expanding, both in the direction of reduced power and toward an increase of power and specific impulse. The two main problems are studied in this paper. The first is to examine the possibility of providing the similarity of plasma parameters in Hall effect thrusters, and the second is to estimate the best achievable output characteristics when scaling Hall effect thrusters. It is shown that a strict similarity of plasma parameters is possible only for the same type of propellant at the same discharge voltage at invariance of at least two dimensionless scaling parameters. Based on the analysis of the similarity criteria and available experimental data, a speculative assertion is made, that in the optimal mode, all the geometrical dimensions of the Hall thruster should be changed in the same proportion. For this type of scaling, the semi-empirical expression for the mass utilization efficiency is obtained under the invariance of the heat flu...