  This paper constructs an analytic framework for calculating the assembly of
galactic disks from the collapse of gas within dark matter halos, with the goal
of determining the surface density profiles. Gas parcels (baryons) fall through
the potentials of dark matter halos on nearly ballistic, zero energy orbits and
collect in a rotating disk. The dark matter halos have a nearly universal form,
as determined previously through numerical simulations. The calculation is
first carried out for a variety of pre-collapse mass distributions and rotation
profiles, including polytropic spheres in hydrostatic equilibrium with the halo
potential. The resulting disk surface density profiles have nearly power-law
forms, with well-defined edges. This idealized scenario is generalized to
include non-spherical starting states and multiple accretion events (due to gas
being added to the halo via merger events). This latter complication is
explored in detail and considers a log-normal distribution for the angular
momenta of the pre-collapse states. If this distribution is wide, then the
composite surface density approaches a universal power-law form, independent of
the shape of the constituent profiles. When the angular momentum distribution
has an intermediate width, the composite surface density attains a nearly
exponential form, roughly consistent with profiles of observed galaxies.
