  We investigate the influence of the network's size on the degree distribution
in Barabasi-Albert model of growing network with initial attractiveness. Our
approach based on spectral moments allows to treat analytically several
variants of the model and to calculate the cut-off function giving finite size
corrections to the degree distribution. We study the effect of initial
configuration as well as of addition more than one link per time step. The
results indicate that asymptotic properties of the cut-off depend only on the
exponent in the power law describing the tail of the degree distribution.
