  To discriminate between different dust formation processes is a key issue in
order to understand its properties. We analysed six submillimeter galaxies at
redshifts 4<z<5 and nine quasars at 5<z<6.4. We estimated their dust masses
from their (sub)millimeter emission and their stellar masses from the spectral
energy distribution modelling or from the dynamical and gas masses obtained
from the CO line detections. We calculated the dust yields per AGB star and per
SN required to explain these dust masses and concluded that AGB stars are not
efficient enough to form dust in the majority of these galaxies. SN could be
responsible for dust production, but only if dust destruction in the SN shocks
is not taken into account. Otherwise even SNe are not efficient enough, which
advocates for some other dust production mechanism. We present the hypothesis
that grain growth in the interstellar medium is responsible for bulk of the
dust mass accumulation in these galaxies.
