Growing Supermassive Black Holes by z = 6 with "Quasistars" Elena Rossi I present my study of the structure and evolution of ``quasistars," accreting black holes embedded within massive hydrostatic gaseous envelopes. The accretion rate onto the black hole adjusts so that the luminosity carried by the convective envelope equals the Eddington limit for the total mass (BH+envelope mass). This greatly exceeds the Eddington limit for the black hole mass alone, leading to rapid growth of the black hole. These stable configurations may model the early growth of supermassive black hole seeds. This would accomodate the presence of bright quasars at redshift greater 6. In this talk, I present analytic models and numerical stellar structure calculations that study the structure and evolution of quasistars. While the black hole mass increases, the photospheric temperature of the envelope decreases with time and it eventually hits a limiting value, analogous to the Hayashi track for red giants and protostars, below which no hydrostatic solution for the convective envelope exists. For metal-free (Population~III) opacities this limiting temperature is approximately 4000 K. After a quasistar reaches this limiting temperature, it is rapidly dispersed by radiation pressure. Black hole seeds with masses between 10^3 and 10^4 solar masses could form via this mechanism in less than a few Myr.