We present a detailed parameter study of collapsing turbulent cloud cores, varying the initial density profile and the initial turbulent velocity field. We systematically investigate the influence of different initial conditions on the star formation process, mainly focusing on the fragmentation, the number of formed stars and the resulting mass distributions. Our study compares four different density profiles (uniform, Bonnor–Ebert type, ρ∝r−1.5 and ρ∝r−2), combined with six different supersonic turbulent velocity fields (compressive, mixed and solenoidal, initialized with two different random seeds each) in three-dimensional simulations using the adaptive-mesh refinement, hydrodynamics code flash. The simulations show that density profiles with flat cores produce hundreds of low-mass stars, either distributed throughout the entire cloud or found in subclusters, depending on the initial turbulence. Concentrated density profiles always lead to the formation of one high-mass star in the centre of the cloud and, if at all, low-mass stars surrounding the central one. In uniform and Bonnor–Ebert type density distributions, compressive initial turbulence leads to local collapse about 25 per cent earlier than solenoidal turbulence. However, central collapse in the steep power-law profiles is too fast for the turbulence to have any significant influence. We conclude that (i) the initial density profile and turbulence mainly determine the cloud evolution and the formation of clusters, (ii) the initial mass function (IMF) is not universal for all setups and (iii) that massive stars are much less likely to form in flat density distributions. The IMFs obtained in the uniform and Bonnor–Ebert type density profiles are more consistent with the observed IMF, but shifted to lower masses.