TCV is a small-sized tokamak, where finite size effects (often called ‘rho-star’ or ‘global’ effects) could significantly impact the heat and particle fluxes, leading to discrepancies between gyrokinetic flux-tube results and global ones [McMillan et al., 2010 Phys. Rev. Lett.]. The impact of global effects on the radial profile of the plasma density has been investigated in a previous study for a particular TCV discharge with negligible particle source, satisfying the ‘zero particle flux’ condition. A radially local flux-tube analysis, reconstructing the dependence of the peaking of the density profile on the main physical parameters, invoking the zero particle flux constraint, was pursued close to mid-radius in [Mariani et al., 2018 Phys. Plasmas]. This analysis was followed by a global one [Mariani et al., 2019 Plasma Phys. Control. Fusion], where local quasi-linear and nonlinear results were compared with global simulations, showing small global effects on the density peaking. However, these gradient-driven global runs considered Krook-type heat and particle sources to keep temperature and density profiles fixed on average, which differ from the experimental radially localized sources. To remove this possible bias on the results, a different evaluation of the density peaking for the same case is performed here, based on global nonlinear hybrid simulations where the temperature profiles are [still] kept fixed with the Krook-type sources, however the density profile relaxes in a flux-driven way (with zero particle source). The new hybrid simulations show a good agreement with the old gradient-driven runs. A global quasi-linear model is also developed and applied using the output from linear global runs, to estimate ratios of fluxes, showing a good agreement with the results of global nonlinear gradient-driven simulations. The effect of collisions on the flux-tube results is also investigated, in order to evaluate their impact on the radial variation of the density peaking.