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Population receptive field (pRF) analysis has become the most popular method for retinotopic mapping with functional magnetic resonance imaging. It requires assumptions about the hemodynamic response function (HRF) to model a voxel’s response. Most pRF studies use canonical HRFs based on normative data or individual HRFs estimated via independent, event-related stimulation paradigms. However, the choice of HRF can influence pRF size estimates substantially (Lerma-Usabiaga et al., 2020, PLOS Comp. Biol. 16(6): e1007924). To understand how this might affect results in practice, here we concurrently fit a double-gamma HRF with five free parameters as part of the pRF model. Using simulated data, we first demonstrate that this algorithm accurately recovers different ground truth HRFs used for generating the data. Next, we reanalyzed several empirical pRF datasets collected using different stimulus paradigms (bar sweeps, combined wedge+ring), magnetic field strengths (1.5T, 3T, 7T), and pulse sequences. Concurrent HRF fitting affected pRF size estimates considerably. It typically improved the presumed validity of model fits by reducing the proportion of artifactually small pRFs. Importantly, the best-fitting HRF varied between datasets. It also differed substantially from all canonical HRFs and from HRFs measured independently, indicative of response non-linearities. Finally, HRF shape also differed substantially between early and higher visual cortex. All these differences could theoretically affect the interpretation of reported findings, such as claims about inhibitory modulation or contextual processing. To test this, we conducted further simulations. Even when the ground truth pRF had a circular Gaussian profile, analyzing these data with an inhibitory surround model (difference of Gaussians pRF) produced spurious estimates of surround inhibition. Such errors were greatly exacerbated when assuming a different HRF than the one used for data generation. Our findings therefore show pRF parameters estimated when assuming a fixed HRF should be treated with caution.