  We consider three-body systems in two dimensions with zero-range interactions
for general masses and interaction strengths. The momentum-space Schr\"odinger
equation is solved numerically and in the Born-Oppenheimer (BO) approximation.
The BO expression is derived using separable potentials and yields a concise
adiabatic potential between the two heavy particles. The BO potential is
Coulomb-like and exponentially decreasing at small and large distances,
respectively. While we find similar qualitative features to previous studies,
we find important quantitative differences. Our results demonstrate that
mass-imbalanced systems that are accessible in the field of ultracold atomic
gases can have a rich three-body bound state spectrum in two dimensional
geometries. Small light-heavy mass ratios increase the number of bound states.
For 87Rb-87Rb-6Li and 133Cs-133Cs-6Li we find respectively 3 and 4 bound
states.
