It is often claimed that there is not only one, but two different types of solar dynamos: the one that is responsible for the appearance of sunspots and the 11-yr cycle, frequently referred to as the “global dynamo”, and a statistically time-invariant dynamo, generally referred to as the “local dynamo”, which is supposed to be responsible for the ubiquitous magnetic structuring observed at small scales. Here we examine the relative contributions of these two qualitatively different dynamos to the small-scale magnetic flux, with the following conclusion: The local dynamo does not play a significant role at any of the spatially resolved scales, nearly all the small-scale flux, including the flux revealed by Hinode, is supplied by the global dynamo. This conclusion is reached by careful determination of the Sun's noise-corrected basal magnetic flux density while making use of a flux cancellation function determined from Hinode data. The only allowed range where there may be substantial or even dominating contributions from a local dynamo seems to be the scales below about 10 km, as suggested by observations of the Hanle depolarization effect in atomic spectral lines. To determine the fraction of the Hanle depolarization that may be due to the action of a local dynamo, a synoptic program is being initiated at IRSOL (Istituto Ricerche Solari Locarno).