A stratocumulus‐to‐cumulus transition as observed in a cold air outbreak over the North Atlantic Ocean is compared in global climate and numerical weather prediction models and a large‐eddy simulation model as part of the Working Group on Numerical Experimentation “Grey Zone” project. The focus of the project is to investigate to what degree current convection and boundary layer parameterizations behave in a scale‐adaptive manner in situations where the model resolution approaches the scale of convection. Global model simulations were performed at a wide range of resolutions, with convective parameterizations turned on and off. The models successfully simulate the transition between the observed boundary layer structures, from a well‐mixed stratocumulus to a deeper, partly decoupled cumulus boundary layer. There are indications that surface fluxes are generally underestimated. The amount of both cloud liquid water and cloud ice, and likely precipitation, are under‐predicted, suggesting deficiencies in the strength of vertical mixing in shear‐dominated boundary layers. But also regulation by precipitation and mixed‐phase cloud microphysical processes play an important role in the case. With convection parameterizations switched on, the profiles of atmospheric liquid water and cloud ice are essentially resolution‐insensitive. This, however, does not imply that convection parameterizations are scale‐aware. Even at the highest resolutions considered here, simulations with convective parameterizations do not converge toward the results of convection‐off experiments. Convection and boundary layer parameterizations strongly interact, suggesting the need for a unified treatment of convective and turbulent mixing when addressing scale‐adaptivity.