  We study the dynamics and growth of dust particles in circumstellar disks of
different masses that are prone to gravitational instability during the
critical first Myr of their evolution. The dust component is made up of two
different components: micron-sized dust and grown dust of evolving size. For
the dust component, we considered the dust coagulation, fragmentation, momentum
exchange with the gas, and dust self-gravity. We found that the micron-sized
dust particles grow rapidly in the circumstellar disk, reaching a few cm in
size in the inner 100 au of the disk during less than 100 kyr after the disk
formation, provided that fragmentation velocity is $30\rm~ms^{-1}$. Due to the
accretion of micron dust particles from the surrounding envelope, which serves
as a micron dust reservoir, the approximately cm-sized dust particles continue
to be present in the disk for more than 900 kyr after the disk formation and
maintain a dust-to-gas ratio close to 0.01. We show that a strong correlation
exists between the gas and pebble fluxes in the disk. We find that radial
surface density distribution of pebbles in the disk shows power-law
distribution with an index similar to that of the Minimum-mass solar nebula
(MMSN) regardless the disk mass. We also show that the gas surface density in
our models agrees well with measurements of dust in protoplanetary disks of AS
209, HD 163296, and DoAr 25 systems. Pebbles are formed during the very early
stages of protoplanetary disk evolution. They play a crucial role in the planet
formation process. Our disc simulations reveal the early onset ($<10^5$ yr) of
an inwards-drifting flux of pebble-sized particles that makes up approximately
between one hundredth and one tenth of the gas mass flux, which appears
consistent with mm-observations of discs. (Abridged)
