  We have developed a theory of quasiparticle backscattering in a system of
point contacts formed between single-mode edges of several Fractional Quantum
Hall Liquids (FQHLs) with in general different filling factors $\nu_j$ and one
common single-mode edge $\nu_0$ of another FQHL. In the strong-tunneling limit,
the model of quasiparticle backscattering is obtained by the duality
transformation of the electron tunneling model. The new physics introduced by
the multi-point-contact geometry of the system is coherent splitting of
backscattered quasiparticles at the point contacts in the course of propagation
along the common edge $\nu_0$. The ``branching ratios'' characterizing the
splitting determine the charge and exchange statistics of the edge
quasiparticles that can be different from those of Laughlin's quasiparticles in
the bulk of FQHLs. Accounting for the edge statistics is essential for the
system of more than one point contact and requires the proper description of
the flux attachement to tunneling electrons.
