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The observations of high redshifts quasars at $z\gtrsim 6$ have revealed thatsupermassive black holes (SMBHs) of mass $\sim 10^9\,\mathrm{M_{\odot}}$ werealready in place within the first $\sim$ Gyr after the Big Bang. Supermassivestars (SMSs) with masses $10^{3-5}\,\mathrm{M_{\odot}}$ are potential seeds forthese observed SMBHs. A possible formation channel of these SMSs is theinterplay of gas accretion and runaway stellar collisions inside dense nuclearstar clusters (NSCs). However, mass loss due to stellar winds could be animportant limitation for the formation of the SMSs and affect the final mass.In this paper, we study the effect of mass loss driven by stellar winds on theformation and evolution of SMSs in dense NSCs using idealised N-bodysimulations. Considering different accretion scenarios, we have studied theeffect of the mass loss rates over a wide range of metallicities$Z_\ast=[.001-1]\mathrm{Z_{\odot}}$ and Eddington factors $f_{\rmEdd}=L_\ast/L_{\mathrm{Edd}}=0.5,0.7,\,\&\, 0.9$. For a high accretion rate of$10^{-4}\,\mathrm{M_{\odot}yr^{-1}}$, SMSs with masses $\gtrsim 10^3\MSun$could be formed even in a high metallicity environment. For a lower accretionrate of $10^{-5}\,\mathrm{M_{\odot}yr^{-1}}$, SMSs of masses $\sim10^{3-4}\,\mathrm{M_{\odot}}$ can be formed for all adopted values of $Z_\ast$and $f_{\rm Edd}$, except for $Z_\ast=\mathrm{Z_{\odot}}$ and $f_{\rm Edd}=0.7$or 0.9. For Eddington accretion, SMSs of masses $\sim 10^3\,\mathrm{M_{\odot}}$can be formed in low metallicity environments with $Z_\ast\lesssim0.01\mathrm{Z_{\odot}}$. The most massive SMSs of masses $\sim10^5\,\mathrm{M_{\odot}}$ can be formed for Bondi-Hoyle accretion inenvironments with $Z_\ast \lesssim 0.5\mathrm{Z_{\odot}}$.

Effect of mass loss due to stellar winds on the formation of supermassive black hole seeds in dense nuclear star clusters