Polarization carries information about the magnetic fields in interstellar clouds. The observations of polarized dust emission are used to study the role of magnetic fields in the evolution of molecular clouds and the initial phases of star-formation. We study the grain alignment with realistic simulations, assuming the radiative torques to be the main mechanism that spins the grains up. The aim is to study the efficiency of the grain alignment as a function of cloud position and to study the observable consequences of these spatial variations. Our results are based on the analysis of model clouds derived from MHD simulations. The continuum radiative transfer problem is solved with Monte Carlo methods to estimate the 3D distribution of dust emission and the radiation field strength affecting the grain alignment. We also examine the effect of grain growth in cores. We are able to reproduce the results of Cho & Lazarian using their assumptions. However, the anisotropy factor even in the 1D case is lower than their assumption of $gamma = 0.7$, and thus we get less efficient radiative torques. Compared with our previous paper, the polarization degree vs. intensity relation is steeper because of less efficient grain alignment within dense cores. Without grain growth, the magnetic field of the cores is poorly recovered above a few $A_{rm V}$. If grain size is doubled in the cores, the polarization of dust emission can trace the magnetic field lines possibly up to $A_{rm V} sim 10$ magnitudes. However, many of the prestellar cores may be too young for grain coagulation to play a major role. The inclusion of direction dependent radiative torque efficiency weakens the alignment. Even with doubled grain size, we would not expect to probe the magnetic field past a few magnitudes in $A_{rm V}$.
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