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We present a numerical study of the evolution of power-law tails (PLTs) inthe (column-)density distributions ($N$-PDF, $\rho$-PDF) in contractingstar-forming clumps in primordial gas, without and with some initial rotationaland/or turbulent support. In all considered runs multiple PLTs emerge shortlyafter the formation of the first protostar. The first PLT (PLT 1) in the$\rho$-PDF is a stable feature with slope $q_1\simeq -1.3$ which corresponds --under the condition of preserved spherical symmetry -- to the outer envelope ofthe protostellar object with density profile $\rho\propto l^{-2}$ in theclassical Larson-Penston collapse model, where $l$ is the radius. The secondPLT (PLT 2) in the $\rho$-PDF is stable in the pure-infall runs but fluctuatessignificantly in the runs with initial support against gravity as dozens ofprotostars form and their mutual tidal forces change the density structure. Itsmean slope, $\langle q_2\rangle\simeq -2$, corresponds to a density profile of$\rho\propto l^{-3/2}$ which describes a core in free fall in the classicalLarson-Penston collapse model or an attractor solution at scales withdominating protostellar gravity. PLT 1 and PLT 2 in the $N$-PDFs are generallyconsistent with the observational data of Galactic low-mass star-formingregions from {\it Herschel} data. In the runs with initial support againstgravity a third PLT (PLT~3) in the $\rho$-PDFs appears simultaneously with orafter the emergence of PLT 2. It is very shallow, with mean slope of $\langleq_3\rangle\simeq -1$, and is associated with the formation of thin protostellaraccretion disks.

Multiple power-law tails in the density and column-density distribution in contracting star-forming clumps