  The description of electron current through a splitting is a mathematical
problem of electron transport in quantum networks. For quantum networks
constructed on the interface of narrow-gap semiconductors the relevant
scattering problem for the multi-dimensional Schoedinger equation may be
substituted by the corresponding problem on a one-dimensional linear graph with
proper selfadjoint boundary conditions at the nodes. However, realistic
boundary conditions for splittings have not yet been derived.
  Here we consider some compact domain attached to a few semi-infinite lines as
a model for a quantum network. An asymptotic formula for the scattering matrix
for this object is derived in terms of the properties of the compact domain.
This allows us to propose designs for devices for manipulating quantum current
through a splitting.
