Chained transistors, how far can you go :)

so i found this ultra high gain probe project:
Ultra High Sensitive Probe

which is basically a 3 step darlington. that got me thinking:
how many transistors can you chain? has anyone here built any insanly high gain amps? if you use some kind of shielding can you make a amp with a gain in the 1000,000,000s?

I don't actually have a project that needs this kind of thing but its interesting because of the ridiculous numbers you could get even if noise,non-linearity ,feedback,etc did make it useless

maybe you could study current flowing in the ground or something?

As you already suggested, noise and leakage would make it useless.

That's what i thought would happen. although with a whole bunch of stages leakage would probable be more significant then noise and just saturate everything. still a cool project even if it stops at 3 stages.
thanks nigel!

A Darlington has a high current gain but the voltage gain is similar to that of one transistor.

Op amps have very high voltage gain, which is usually reduced to something usable with feedback.