  We assess the most plausible scenarios for generating large amounts of dust
in high-z quasars (QSOs) on the basis of observationally derived physical
properties of QSOs at z > 6. We use a chemical evolution model to compute the
temporal progression of quantities, such as the amount of dust and gas, stellar
masses, star formation rates (SFRs) and the metallicity for various
combinations of the initial mass function (IMF), the mass of the galaxy, dust
production efficiencies, and the degree of dust destruction in the ISM. We
investigate the influence of the SFR on the evolution of these quantities, and
determine the earliest epochs at which agreement with observations can be
achieved. We apply the obtained results to individual QSOs at z > 6. We find
that large quantities of dust can be generated rapidly as early as 30 Myr after
the onset of the starburst when the SFR of the starburst is > 10^3 M_sun
yr^(-1). The amount of dust and several other physical quantities of individual
QSOs at z > 6 are satisfactorily reproduced by models at epochs 30, 70, 100,
and 170 Myr for galaxies with initial gas masses of 1-3 x 10^11 M_sun. The best
agreement with observations is obtained with top-heavy IMFs. A sizable dust
contribution from supernovae (SNe) is however required, while at these epochs
dust production by asymptotic giant branch (AGB) stars is negligible. Moderate
dust destruction in the ISM can be accommodated.
