  Galaxy mergers represent a fundamental physical process under hierarchical
structure formation, but their role in triggering AGNs is still unclear. We aim
to investigate the merger-AGN connection using state-of-the-art observations
and novel methods in detecting mergers and AGNs. We selected stellar
mass-limited samples at redshift z<1 from KiDS, focusing on the KiDS-N-W2 field
with a wide range of multi-wavelength data. Three AGN types, selected in the
MIR, X-ray, and via SED modelling, were analysed. To identify mergers, we used
convolutional neural networks trained on two cosmological simulations. We
created mass and redshift-matched control samples of non-mergers and non-AGNs.
We observe a clear AGN excess (a factor of 2-3) in mergers with respect to
non-mergers for the MIR AGNs, and a mild excess for the X-ray and SED AGNs,
indicating that mergers could trigger all 3 types but are more connected with
the MIR AGNs. About half of the MIR AGNs are in mergers but it is unclear
whether mergers are the main trigger. For the X-ray and SED AGNs, mergers are
unlikely to be the dominant trigger. We also explore the relation using the
continuous AGN fraction $f_{AGN}$ parameter. Mergers exhibit a clear excess of
high $f_{AGN}$ values relative to non-mergers, for all AGNs. We unveil the
first merger fraction $f_{merg}-f_{AGN}$ relation with two distinct regimes.
When the AGN is not dominant, the relation is only mildly increasing or even
flat, with the MIR AGNs showing the highest $f_{merg}$. In the regime of very
dominant AGNs ($f_{AGN}\geq0.8$), $f_{merg}$ shows a steeply rising trend with
increasing $f_{AGN}$ for all AGN types. These trends are also seen when plotted
against AGN bolometric luminosity. We conclude that mergers are most connected
with dust-obscured AGNs (linked to a fast-growing phase of the SMBH) and are
the main or even the sole fuelling mechanism of the most powerful AGNs.
