  We investigate the three-body properties of two identical "up" fermions and
one distinguishable "down" atom interacting in a strongly confined
two-dimensional geometry. We compute exactly the atom-dimer scattering
properties and the three-body recombination rate as a function of collision
energy and mass ratio m_up/m_down. We find that the recombination rate for
fermions is strongly energy dependent, with significant contributions from
higher partial waves at low energies. For m_up < m_down, the s-wave atom-dimer
scattering below threshold is completely described by the scattering length.
Furthermore, we examine the "up-up-down" bound states (trimers) appearing at
large m_up/m_down and find that the energy spectrum for the deepest bound
trimers resembles that of a hydrogen atom confined to two dimensions.
