This paper describes three-dimensional (3D) large eddy simulations of stellar surface convection using realistic model physics. The simulations include the present Sun, a subgiant of one solar mass and a lower-gravity subgiant, also of one solar mass. We examine the thermal structure (superadiabaticity) after modification by 3D turbulence, the overshoot of convective motions into the radiative atmosphere and the range of convection cell sizes. Differences between models based on the mixing length theory (MLT) and the simulations are found to increase significantly in the more evolved stages as the surface gravity decreases. We find that the full width at half maximum (FWHM) of the turbulent vertical velocity correlation provides a good objective measure of the vertical size of the convective cells. Just below the convection surface, the FWHM is close to the mean vertical size of the granules and 2 × FWHM is close to the mean horizontal diameter of the granules. For the Sun, 2 × FWHM = 1200 km, a value close to the observed mean granule size. For all the simulations, the mean horizontal diameter is close to 10 times the pressure scaleheight at the photospheric surface, in agreement with previous work.