(Abridged) Aim: We attempt to determine robust estimates of the heliospheric magnetic flux ($Phi_H$) using Parker Solar Probe (PSP) data, analyze how susceptible this is to overestimation compared to the true open flux ($Phi_{open}$), assess its dependence on time and space, and compare it to simple estimates from Potential Field Source Surface (PFSS) models. Methods: We compare different methods of computation using data from PSP, STEREO A and Wind. The effects of fluctuations and large scale structure on the estimate are probed by using measured radial trends to produce synthetic data. Best estimates are computed as a function of time and space, and compared to estimates from PFSS models. Results: Radially-varying fluctuations of the HMF vector and variation of the Parker spiral angle cause the standard metrics of the mean and mode to evolve with radius independent of the central value about which the vector fluctuates. This is best mitigated by projecting the vector into the background Parker spiral direction. Nevertheless, we find a small enhancement in flux close to 1AU. The fraction of locally inverted field lines grows with radial distance from the Sun which remains a possible physical reason for this excess, but is negligible at PSP`s perihelia. Similarly, the impact of fluctuations in general is much reduced at PSP`s perihelia. The overall best estimate is ~2.5 nT AU2 . No strong dependence on latitude or longitude is apparent. The PFSS models predict lower values from 1.2 to 1.8 nT AU2. Conclusions: The heliospheric flux is robustly estimated relative to a mean Parker spiral direction at PSP`s perihelia where the decay of fluctuations and weakening importance of local flux
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