  The Efimov effect for three bosons in three dimensions requires two
infinitely large $s$-wave scattering lengths. We assume two identical particles
with very large scattering lengths interacting with a third particle. We use a
novel mathematical technique where the centrifugal barrier contains an
effective dimension parameter, which allows efficient calculations precisely as
in ordinary three spatial dimensions. We investigate properties and occurrence
conditions of Efimov states for such systems as functions of the third
scattering length, the non-integer dimension parameter, mass ratio between
unequal particles, and total angular momentum. We focus on the practical
interest of the existence, number of Efimov states and their scaling
properties. Decreasing the dimension parameter from $3$ towards $2$ the Efimov
effect and states disappear for critical values of mass ratio, angular momentum
and scattering length parameter. We investigate the relations between the four
variables and extract details of where and how the states disappear. Finally,
we supply a qualitative relation between the dimension parameter and an
external field used to squeeze a genuine three dimensional system.
