Evolution of the kernel magnitude maps of a kernel-nuller at the focus of the four VLTI UTs, observing the ±15 mas FOV surrounding the target HIP 107773. The figure shows four blocks of maps altogether, which provide insights into the behaviour of the kernel outputs. The first block (red contour, top left) of 54 maps shows how the magnitude maps of the three kernel-nuller outputs evolve over a ±4 h observing period centred on the target transit time (h = 0). We can see the transmission patterns gradually rotating in a clockwise direction with time, scanning the FOV to intercept the light of any off-axis feature of the astrophysical scene. A white star in each plot marks the location of the central star where the transmission for all channels is equal to zero, by design. The second block (pink contour, rightmost column) of three maps shows the time-average of each kernel output magnitude map. The third block (blue contour, bottom row) of nine maps shows how at any instant, the sum of all kernel magnitude maps is spatially distributed. Summing the kernel outputs shows that the overall instantaneous sensitivity of the nuller is much more uniform over the FOV, even if it nevertheless systematically features off-axis replicas of the on-axis null, which are referred to as transmission holes. The fourth block (green contour, single bottom-right map) shows the time-averaged global throughput, which reveals that with a sufficiently wide observing window, the FOV is uniformly covered, and the nuller will be able to capture the light of a companion regardless of where it may reside. All maps share the same colour scale where the transmission is expressed in units of the kernel amplitude collected by one telescope.