  This work is aimed by the spirit of 1946 Moran's Theorem, which ensures that
both the box and the Hausdorff dimensions for any attractor could be calculated
as the solution of an equation involving only its similarity factors. To
achieve such result, the open set condition (OSC, herein) is required to be
satisfied by the pieces of the attractor in order to guarantee that they do not
overlap too much. In this paper, we generalize the classical Moran's through a
fractal dimension model which allows to obtain the fractal dimension of any
IFS-attractor equipped with its natural fractal structure without requiring the
OSC to be satisfied.
