CDFs of the fraction of BNS mergers within the observed offset F. Upper panels: Comparison of models with different natal kick prescriptions, namely the Hobbs model (left column), the Verbunt model (central column), and the Bray model (right column). Distributions in the first row are modelled with Sérsic profiles, while those in the second row are modelled with the mass-size relation. The KS p-value for each CDF with respect to a uniform distributions is shown in each panel. Host types and stellar distribution models are shown in the legend. Lower panels: Comparison of host subsamples at different P_ch thresholds, namely ≤20% (left column), ≤10% (central column), and ≤2% (right column). All the remaining assumptions are fiducial; in particular, we are using the Verbunt model for natal kicks.