  Universal properties of mass-imbalanced three-body systems in 2D are studied
using zero-range interactions in momentum space. The dependence of the
three-particle binding energy on the parameters (masses and two-body energies)
is highly non-trivial even in the simplest case of two identical particles and
a distinct one. This dependence is parametrized for ground and excited states
in terms of {\itshape supercircles} functions in the most general case of three
distinguishable particles.
