  We present new evolutionary models of primordial very massive stars, with
initial masses ranging from $100\,\mathrm{{M}_{\odot}}$ to
$1000\,\mathrm{{M}_{\odot}}$, that extend from the main sequence until the
onset of dynamical instability caused by the creation of electron-positron
pairs during core C, Ne, or O burning, depending on the star's mass and
metallicity. Mass loss accounts for radiation-driven winds as well as
pulsation-driven mass-loss on the main sequence and during the red supergiant
phase. After examining the evolutionary properties, we focus on the final
outcome of the models and associated compact remnants. Stars that avoid the
pair-instability supernova channel, should produce black holes with masses
ranging from $\approx 40\, \mathrm{{M}_{\odot}}$ to $\approx
1000\,\mathrm{{M}_{\odot}}$. In particular, stars with initial masses of about
$100\,\mathrm{{M}_{\odot}}$ could leave black holes of $\simeq 85-90\,
\mathrm{{M}_{\odot}}$, values consistent with the estimated primary black hole
mass of the GW190521 merger event. Overall, these results may contribute to
explain future data from next-generation gravitational-wave detectors, such as
the Einstein Telescope and Cosmic Explorer, which will have access to as-yet
unexplored BH mass range of $\approx 10^2-10^4\,\mathrm{{M}_{\odot}}$ in the
early universe.
