A method to study weakly bound three-body quantum systems in two dimen
sions is formulated in coordinate space for short-range potentials. Oc
currences of spatially extended structures (halos) are investigated. B
orromean systems are shown to exist in two dimensions for a certain cl
ass of potentials. An extensive numerical investigation shows that a w
eakly bound two-body state gives rise to two weakly bound three-body s
tates, a reminiscence of the Efimov effect in three dimensions. The pr
operties of these two states in the weak binding limit turn out to be
universal.