  In the framework of the Glauber approach we analyze the shape parameters of
the early-formed system and their event-by-event fluctuations. We test a
variety of models: the conventional wounded nucleon model, a model admixing
binary collisions to the wounded nucleons, a model with hot spots, as well as
the hot-spot model where the deposition of energy occurs with a superimposed
probability distribution. We look in detail at the so-called participant
multipole moments, obtained by an averaging procedure where in each event the
system is translated to its center of mass and aligned with the major principal
axis of the ellipse of inertia. Quantitative comparisons indicate substantial
relative effects for eccentricity in variants of Glauber models. On the other
hand, the dependence of the scaled standard deviation of the participant
eccentricity on the chosen model is weak. For all models the values range from
about 0.5 for the central collisions to about 0.3-0.4 for peripheral
collisions, both for the gold-gold and copper-copper collisions. They are
dominated by statistics and change only by 10-15% from model to model. We
provide an approximate analytic expansion for the multipole moments and their
fluctuations given in terms of the fixed-axes moments. For central collisions
and in the absence of correlations it gives the simple formula for the scaled
standard deviation of the participant eccentricity: sqrt(4/pi-1). Similarly, we
obtain expansions for the radial profiles of the multipole distributions. We
investigate the relevance of the shape-fluctuation effects for jet quenching
and find them important only for very central events. Finally, we argue how
smooth hydro leads to the known result v_4 ~ v_2^2, and further to the
prediction Delta v_4/v_4 = 2 Delta v_2/v_2.
