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Planetary formation theories and, more specifically, migration models predictthat planets can be captured in mean-motion resonances (MMRs) during the discphase. The distribution of period ratios between adjacent planets shows anaccumulation in the vicinity of the resonance, which is not centred on thenominal resonance but instead presents an offset slightly exterior to it. Herewe extend on previous works by thoroughly exploring the effect of differentdisc and planet parameters on the resonance offset during the disc migrationphase. The dynamical study is carried out for several first-order MMRs and forboth low-mass Earth-like planets undergoing type-I migration and giant planetsevolving under type-II migration. We find that the offset varies with timeduring the migration of the two-planet system along the apsidal corotationresonance family. The departure from the nominal resonance increases for higherplanetary masses and stronger eccentricity damping. In the Earth to super-Earthregime, we find offset values in agreement with the observations when using asophisticated modelling for the planet-disc interactions, where the dampingtimescale depends on the eccentricity. This dependence causes a feedback whichinduces an increase of the resonance offsets. Regarding giant planets, theoffsets of detected planet pairs are well reproduced with a classical$K$-factor prescription for the planet-disc interactions when the eccentricitydamping rate remains low to moderate. In both regimes, eccentricities are inagreement with the observations too. As a result, planet-disc interactionsprovide a generic channel to generate the offsets found in the observations.

Proximity of exoplanets to first-order mean-motion resonances