  We study a system consisting of a junction of N quantum wires, where the
junction is characterized by a scalar S-matrix, and an impurity spin is coupled
to the electrons close to the junction. The wires are modeled as weakly
interacting Tomonaga-Luttinger liquids. We derive the renormalization group
equations for the Kondo couplings of the spin to the electronic modes on
different wires, and analyze the renormalization group flows and fixed points
for different values of the initial Kondo couplings and of the junction
S-matrix (such as the decoupled S-matrix and the Griffiths S-matrix). We
generally find that the Kondo couplings flow towards large and
antiferromagnetic values in one of two possible ways. For the Griffiths
S-matrix, we study one of the strong coupling flows by a perturbative expansion
in the inverse of the Kondo coupling; we find that at large distances, the
system approaches the ferromagnetic fixed point of the decoupled S-matrix. For
the decoupled S-matrix with antiferromagnetic Kondo couplings and weak
inter-electron interactions, the flows are to one of two strong coupling fixed
points in which all the channels are strongly coupled to each other through the
impurity spin. But strong inter-electron interactions, with K_\rho < N/(N+2),
stabilize a multi-channel fixed point in which the coupling between different
channels goes to zero. We have also studied the temperature dependence of the
conductance at the decoupled and Griffiths S-matrices.
