  We introduce a new quantum transport formalism based on a map of a real
3-dimensional lead-conductor-lead system into an effective 1-dimensional
system. The resulting effective 1D theory is an in principle exact formalism to
calculate the conductance. Besides being more efficient than the principal
layers approach, it naturally leads to a 5-partitioned workbench (instead of 3)
where each part of the device (the true central device, the ballistic and the
non-ballistic leads) is explicitely treated, allowing better physical insight
into the contact resistance mechanisms. Independently, we derive a generalized
Fisher-Lee formula and a generalized Meir-Wingreen formula for the correlated
and uncorrelated conductance and current of the system where the initial
restrictions to ballistic leads are generalized to the case of resistive
contacts. We present an application to graphene nanoribbons.
