  A method to study weakly bound three-body quantum systems in two dimensions
is formulated in coordinate space for short-range potentials. Occurrences of
spatially extended structures (halos) are investigated. Borromean systems are
shown to exist in two dimensions for a certain class of potentials. An
extensive numerical investigation shows that a weakly bound two-body state
gives rise to two weakly bound three-body states, a reminiscence of the Efimov
effect in three dimensions. The properties of these two states in the weak
binding limit turn out to be universal.
  PACS number(s): 03.65.Ge, 21.45.+v, 31.15.Ja, 02.60Nm
