We study the magnetic flux carried by pores located outside active regions with sunspots and investigate their possible contribution to the reversal of the global magnetic field of the Sun. We find that they contain a total flux of comparable amplitude to the total magnetic flux contained in polar caps. The pores located at distances of 40--100~Mm from the closest active region have systematically the correct sign to contribute to the polar cap reversal. These pores can predominantly be found in bipolar magnetic regions. We propose that during grand minima of solar activity, such a systematic polarity trend, akin to a weak magnetic (Babcock-Leighton-like) source term could still be operating but was missed by the contemporary observers due to the limited resolving power of their telescopes.
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