Now what happened? I unpacked the printer, tried not to overlook the last adhesive tape that was plastered all over the place, shook the cartridges as per getting started, installed the software, drives, network-access, ICM profiles and what have you. After 20% of the ink was sucked up in the initialization process and the first internal test-page was produced I and the printer were good to go.
... I thought!
I won't tell you how much paper and ink and time I wasted trying to get the perfect black from this image.

Eisstock-Schiessen 28311 by Thomas, on Flickr
As you can see the sky is a totally black with no structure at all. But all I got was a blotched black on my glossy photo paper. Tried a lot of driver- and profile-tweaking but to no avail.
Finally ...
I switched from Canon to Epson paper.
... and then it worked ::)
I'll try to get a good macro shot at how big the difference is between the two papers.
B.t.w.: The maintenance cartridge of the 3880 is easily user replaceable but was also wasted 44% during the priming stage. Each cartridge has 80ml and there are nine of them. So total ink intake during initialization was around 140ml.