Pretty amazing, even for me. All loggings were done with the same '98 81kW TDI on the same day.
Conclusion? It seems that even a very old and very bad MAF is still usable and will perform like a new one with a little help of a tiny boost circuit.
How is it connected
The output wire of the MAF (pin 5 of Bosch MAF) is cut and the circuit below is inserted. The wire coming from the MAF connects to the wire with label 'From MAF' and the wire that goes to the ECU is connected to the wire 'To ECU'. The 5V supply voltage of this circuit is taken from the MAF connector too. It only draws a current of a few mA.