The paper investigates the properties of reduced order models obtained by projection of a high order system. It answers questions such as are any two models of different orders related by a projection? Is it possible to obtain the same reduced order model using different projections? Etc. It is shown that in cases where not all models of a certain reduced order can be obtained by a projection, the optimal L2 reduced order model is obtained by a unique projection, and it resides on the boundary of the set of attainable models.