The tokamak `a configuration variable (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. 105 155001). 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' (ZPF) condition. A radially local flux-tube analysis, reconstructing the dependence of the peaking of the density profile on the main physical parameters, invoking the ZPF constraint, was pursued close to mid-radius in (Mariani et al 2018 Phys. Plasmas 25 012313). This analysis was followed by a global one (Mariani et al 2019 Plasma Phys. Control. Fusion 61 064005), where local quasi-linear (QL) and nonlinear (NL) results were compared with global simulations, showing small global effects on the density peaking. However, these gradient-driven (GD) 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 NL 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 GD runs. A global QL model is also developed and applied using the output from linear global runs, to estimate ratios of fluxes, showing a good agreement with the flux-tube results of global NL GD simulations. The effect of collisions on the results is also investigated, in order to evaluate their impact on the radial variation of the density peaking.