  We present evolutionary models of massive, accreting population III stars
with constant and variable accretion rates until the end of silicon burning,
with final masses of 1000 - 3000 Msol. In all our models, after the
core-hydrogen-burning phase, the star expands towards the red side of the
Hertzsprung-Russell diagram is where it spends the rest of its evolution.
During core helium burning, the models exhibit an outer convective envelope as
well as many large intermediate convective zones.These intermediate zones allow
for strong internal mixing to occur which enriches the surface in helium. The
effect of increasing metallicity at a constant accretion rate of 10^{-3}
Msol/yr shows an increase in the lifetime, final mass and distribution of
helium in the envelope. Our fiducial model with mass of 3000 Msol has a final
surface helium abundance of 0.74 and 9% of its total mass or 50% of the core
mass, has a value of Gamma1 < 4/3 at the end of core silicon burning. If the
collapse of the core is accompanied by the ejection of the envelope above the
carbon-oxygen core, this could have a significant impact on the chemical
evolution of the surroundings and subsequent stellar generations. The model has
a final log(N/O) ~ 0.45, above the lower limit in the recently detected
high-redshift galaxy GN-z11. We discuss the impact of a single 3000 Msol star
on chemical, mechanical and radiative feedback, and present directions for
future work.
