  We are interested in the tail behavior of the pdf of mass density within the
one and $d$-dimensional Burgers/adhesion model used, e.g., to model the
formation of large-scale structures in the Universe after baryon-photon
decoupling. We show that large densities are localized near ``kurtoparabolic''
singularities residing on space-time manifolds of codimension two ($d \le 2$)
or higher ($d \ge 3$). For smooth initial conditions, such singularities are
obtained from the convex hull of the Lagrangian potential (the initial velocity
potential minus a parabolic term). The singularities contribute {\em
\hbox{universal} power-law tails} to the density pdf when the initial
conditions are random. In one dimension the singularities are preshocks
(nascent shocks), whereas in two and three dimensions they persist in time and
correspond to boundaries of shocks; in all cases the corresponding density pdf
has the exponent -7/2, originally proposed by E, Khanin, Mazel and Sinai (1997
Phys. Rev. Lett. 78, 1904) for the pdf of velocity gradients in one-dimensional
forced Burgers turbulence. We also briefly consider models permitting particle
crossings and thus multi-stream solutions, such as the Zel'dovich approximation
and the (Jeans)--Vlasov--Poisson equation with single-stream initial data: they
have singularities of codimension one, yielding power-law tails with exponent
-3.
