It really does seem to be about the size of your (currency) base

As part of the series of updates I mentioned earlier using the currency component of the monetary base (neglecting reserves), I'm updating the money graph from this post:

I switched Sweden out for the UK (since I had currency component data for the latter, not the former), but it actually seems to work even better than before. One can see the diminishing inflation returns from monetary expansion as the data points turn over near MB = MB0 (σ = 1).