  Properties of candidate stars, forming out of molecular clouds, depend on the
ambient conditions of the parent cloud. We present a series of 2D and 3D
simulations of fragmentation of molecular clouds in starburst regions as well
as clouds under conditions in dwarf galaxies, leading to the formation of
protostellar cores. We explore in particular the metallicity dependence of
molecular cloud fragmentation and the possible variations in the dense core
mass function, as the expression of a multi-phase ISM, due to dynamic and
thermodynamic effects in starburst and metal-poor environments. To study the
level of fragmentation during the collapse, the adaptive mesh refinement code
FLASH is used. With this code, including self-gravity, thermal balance,
turbulence and shocks, collapse is simulated with four different metallicity
dependent cooling functions. Turbulent and rotational energies are considered
as well. During the simulations, number densities of 10^8-10^9 cm^-3 are
reached. The influences of dust and cosmic ray heating are investigated and a
comparison to isothermal cases is made. The presented results indicate that
fragmentation increases with metallicity, while cosmic ray and gas-grain
collisional heating counteract this. We also find that modest rotation and
turbulence can impact the cloud evolution as far as fragmentation is concerned.
In this light, we conclude that radiative feedback, in starburst regions, will
inhibit fragmentation, while low-metallicity dwarfs also should enjoy a star
formation mode in which fragmentation is suppressed.
