  The spectacular results provided by the second-generation VLTI instruments
GRAVITY and MATISSE on active galactic nuclei (AGN) trigger and justify a
strong increase in the sensitivity limit of optical interferometers. A key
component of such an upgrade is off-axis fringe tracking. To evaluate its
potential and limitations, we describe and analyse its error budget including
fringe sensing precision and temporal, angular and chromatic perturbations of
the piston. The global tracking error is computed using standard seeing
parameters for different sites, seeing conditions and telescope sizes for the
current GRAVITY Fringe Tracker (GFT) and a new concept of Hierarchical Fringe
Tracker. Then, it is combined with a large catalogue of guide star candidates
from Gaia to produce sky coverage maps that give the probability to find a
usable off-axis guide star in any part of the observable sky. These maps can be
used to set the specifications of the system, check its sensitivity to seeing
conditions, and evaluate the feasibility of science programs. We check the
availability of guide stars and the tracking accuracy for a large set of 15 799
Quasars to confirm the feasibility of a large program on Broad Line Regions in
the K band with the GFT and show how it can be extended to the L, M, and N
bands. Another set of 331 well-characterized nearby AGNs shows the high
potential of MATISSE for imaging and characterization of the dust torus in the
N band under off-axis tracking on both Unit Telescopes and Auxiliary
Telescopes.
