  We provide a theoretical study of the conductance response of systems based
on graphene nanoribbon to the potential of a scanning probe. The study is based
on the Landauer approach for the tight-binding Hamiltonian with an
implementation of the quantum transmitting boundary method and covers
homogenous nanoribbons, their asymmetric narrowing and quantum point contacts
of various profiles. The response maps at low Fermi energies resolve formation
of n-p junctions induced by the probe potential and a presence of
zigzag-armchair segments of the edges for inhomogeneous ribbons. For an
asymmetric narrowing of the nanoribbons the scanning probe resolves formation
of standing waves related to backscattering within the highest subband of the
narrower part of the system. The QPCs containing a long constriction support
formation of localized resonances which induce a system of conductance peaks
that is reentrant in the Fermi energy, with the form of the probability density
that can be resolved by the conductance mapping. For shorter constrictions the
probe induces smooth conductance minima within the constrictions. In general,
besides the low-energy transport gap, in the wider parts of the ribbon the
variation of the conductance of the system is low compared to the narrower
part.
