  We discuss the structure of the ``forward visible'' (FW) parts of double and
skewed distributions related to usual distributions through reduction
relations. We use factorized models for double distributions (DDs) f(x, alpha)
in which one factor coincides with the usual (forward) parton distribution and
another specifies the profile characterizing the spread of the longitudinal
momentum transfer. The model DDs are used to construct skewed parton
distributions (SPDs). For small skewedness, the FW parts of SPDs H(x, xi) can
be obtained by averaging forward parton densities f(x- xi alpha) with the
weight rho (alpha) coinciding with the profile function of the double
distribution f(x, alpha) at small x. We show that if the x^n moments f_n
(alpha) of DDs have the asymptotic (1-alpha^2)^{n+1} profile, then the
alpha-profile of f (x,alpha) for small x is completely determined by small-x
behavior of the usual parton distribution. We demonstrate that, for small xi,
the model with asymptotic profiles for f_n (alpha) is equivalent to that
proposed recently by Shuvaev et al., in which the Gegenbauer moments of SPDs do
not depend on xi. We perform a numerical investigation of the evolution
patterns of SPDs and gave interpretation of the results of these studies within
the formalism of double distributions.
