  The existence of the Efimov effect is drastically affected by the
dimensionality of the space in which the system is embedded. The effective
spatial dimension containing an atomic cloud can be continuously modified by
compressing it in one or two directions. In the present article we determine
for a general $AAB$ system formed by two identical bosons $A$ and a third
particle $B$ in the two-body unitary limit, the dimensionsality $D$ for which
the Efimov effect can exist for different values of the mass ratio
$\mathpzc{A}=m_B/m_A$. In addition, we provide a prediction for the Efimov
discrete scaling factor, ${\rm exp}\,(\pi/s)$, as a function of a wide range of
values of $\mathpzc{A}$ and $D$, which can be tested in experiments that can be
realized with currently available technology.
