  We discuss the conductance of quantum wires (QW) in terms of the
Tomonaga-Luttinger liquid (TLL) theory. We use explicitly the charge
fractionalization scheme which results from the chiral symmetry of the model.
We suggest that results of the standard two-terminal (2T) conductance
measurement depend on the coupling of TLL with the reservoirs and can be
interpreted as different boundary conditions at the interfaces. We propose a
three-terminal (3T) geometry in which the third contact is connected weakly to
the bulk of TLL subjected to a large bias current. We develop a renormalization
group (RG) analysis for this problem by taking explicitly into account the
splitting of the injected electronic charge into two chiral irrational charges.
We study in the presence of {\it bulk} contact the leading order corrections to
the conductance for two different boundary conditions, which reproduce in the
absence of {\it bulk} contact, respectively, the standard 2T source-drain (SD)
conductance $G_{\rm SD}^{(2)}=e^2/h$ and $G_{\rm SD}^{(2)}=ge^2/h$, where $g$
is the TLL charge interaction parameter. We find that under these two boundary
conditions for the {\it end} contacts the 3T SD conductance $G_{\rm SD}^{(3)}$
shows an UV-relevant deviation from the above two values, suggesting new fixed
points in the ohmic limit. Non-trivial scaling exponents are predicted as a
result of electron fractionalization.
