At laser intensities above 10 23 W/cm 2 the interaction of a laser with a plasma is qualitatively different to the interactions at lower intensities. In this intensity regime solid targets start to become relativistically underdense, gamma-ray production by synchrotron emission starts to become an important feature of the dynamics and, at even higher intensities, electron-positron pair production by the non-linear Breit-Wheeler process starts to occur. Previous work in this intensity regime has considered ion acceleration 1 , 2 , identified different mechanisms for the underlying plasma physics of laser generation of gamma-rays 3 , 4 , 5 considered the effect of target parameters on gamma-ray generation 6 and considered the creation of solid density positronium plasma 3 . However a complete linked understanding of the important new physics of this regime is still lacking. In this paper, an analysis is presented of the effects of target density, laser intensity, target preplasma properties and other parameters on the conversion efficiency, spectrum and angular distribution of gamma-rays by synchrotron emission. An analysis of the importance of Breit-Wheeler pair production is also presented. Target electron densities between 10 22 cm −3 and 5×10 24 cm −3 and laser intensities covering the range between 10 21 W/cm 2 (available with current generation laser facilities) and 10 24 W/cm 2 (upper intensity range expected from the ELI facility) are considered. It is found that peak efficiency of conversion of laser energy into gammaray energy is achieved when the target density is 0.1 times the relativistically corrected critical density and that higher efficiency is obtained at higher laser intensity. Target front surface preplasmas of sufficient length are found to increase the efficiency of gamma-ray production compared with striking overdense solid targets directly in a fashion comparable to that in Nakamura et al. 6 by ensuring that the laser pulse interacts with a plasma of the optimum density. However maximum laser conversion to gamma-rays is achieved by striking a uniform target of the optimum density or a preplasma of sufficient length that the preplasma is nearly a uniform slab. It is found that the efficiency of Breit-Wheeler pair production is not related to either relativistic transparency or efficiency of gamma-ray production but is maximized by striking a high density target with the most intense laser possible. A qualitative model for this behaviour is presented. An analysis of the behavior of the longitundal motion of electrons as target density and laser intensity change is presented and it is found that there are two distinct regimes separated by the ratio of the relativistically corrected plasma frequency to the laser frequency. It is found that the transition between the two regimes is related to the structure of the electron phase space at the head of the laser.