We have examined the resolved stellar populations at large galactocentric distances along the minor axis (from 10 kpc up to between 40 and 75 kpc), with limited major axis coverage, of six nearby highly-inclined Milky Way-mass disc galaxies using HST data from the GHOSTS survey. We select red giant branch stars to derive stellar halo density profiles. The projected minor axis density profiles can be approximated by power laws with projected slopes of between $-2$ and $-3.7$ and a diversity of stellar halo masses of $1-6\times 10^{9}M_{\odot}$, or $2-14\%$ of the total galaxy stellar masses. The typical intrinsic scatter around a smooth power law fit is $0.05-0.1$ dex owing to substructure. By comparing the minor and major axis profiles, we infer projected axis ratios $c/a$ at $\sim 25$ kpc between $0.4-0.75$. The GHOSTS stellar haloes are diverse, lying between the extremes charted out by the (rather atypical) haloes of the Milky Way and M31. We find a strong correlation between the stellar halo metallicities and the stellar halo masses. We compare our results with cosmological models, finding good agreement between our observations and accretion-only models where the stellar haloes are formed by the disruption of dwarf satellites. In particular, the strong observed correlation between stellar halo metallicity and mass is naturally reproduced. Low-resolution hydrodynamical models have unrealistically high stellar halo masses. Current high-resolution hydrodynamical models appear to predict stellar halo masses somewhat higher than observed but with reasonable metallicities, metallicity gradients and density profiles.

26 pages, 17 figures. Accepted for publication in MNRAS