[en] Primordial black holes (PBH) are assumed to be originated at a moment of time of order of the Planck one t sub(pl) -- 10^-43s. Then the gravitational accretion, the capture collisions and the quantum evaporation of PBH's determine an evolution of the PBH mass distribution function and the rate of the cosmic expansion. It was found by analytic and computer calculations that mainly two parameters, namely zeta₀<<1 -the ratio of the initial number of PBH's to the initial entropy of the universe- and K- a factor of order of unity before the integral of collisions- are of value for this cosmological model. Taking into consideration the observed baryon to radiation ratio αsub(obs) = 10^-8 one obtains that the end of the PBH-dominant era was at the moment t sub(fin) -- αsub(obs)sup(-9/4)t sub(pl) and the greatest PBH's evaporated earlier than t sub(max) -- αsub(obs)sup(-27/4)t sub(pl) -- 10¹¹s. The spectrum of PBH masses in the case K<1 was found to be exponential and stable to a change of initial conditions. (auth.)