Context :

Aims : We intend to 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 \gtrsim 6 .

Methods : 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 \gtrsim 6 .

Results : 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 \gtrsim 10 ^ { 3 } \mathrm { M } _ { \odot } yr ^ { -1 } .
The amount of dust and several other physical quantities of individual QSOs at z \gtrsim 6 are satisfactorily reproduced by models at epochs 30 , 70 , 100 , and 170 Myr for galaxies with initial gas masses of 1–3 \times 10 ^ { 11 } \mathrm { M } _ { \odot } .
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 .

Conclusions :