  The collapse of marginally bound, inhomogeneous, pressureless (dust) matter,
in spherical symmetry, is considered. The starting point is not, in this case,
the integration of the Einstein equations from some suitable initial
conditions. Instead, starting from the corresponding general exact solution of
these equations, depending on two arbitrary functions of the radial coordinate,
the fulfillment of the Lichnerowicz matching conditions of the interior
collapsing metric and the exterior Schwarzschild one is tentatively assumed
(the continuity of the metric and its first derivatives on the time-like
hypersurface describing the evolution of the spherical 2-surface boundary of
the collapsing cloud), and the consequences of such a tentative assumption are
explored. The whole analytical family of resulting models is obtained and some
of them are picked out as physical better models on the basis of the finite and
constant value of its {\em intrinsic} energy.
