Wikipedia Definition:
Hartig net is a hyphal network, that extends into the root, penetrating between epidermal and cortical cells. This network is a site of nutrient exchange between the fungus and the hostplant.[1] Hartig net is typical for ectomycorrhiza. The early research on the anatomy of the interface between ectomycorrhizal fungi and plants was done by Robert Hartig, a 19th-century German plant pathologist, so the Hartig net is named after him.
For reference some internet images for a Hartig net:
Now my images...
"Y" forming from a hair:
Net draped around hair:
Different branching formations:
Some are almost phantom like:
Formed around a hair shaft/root:
Since I’m no expert I can only guess which kind of fungus this could be. I have a theory, but that's another post...
Here's a long but thought provoking read on beneficial and pathogenic roles fungus can play:
http://www.apsnet.org/edcenter/intropp/PathogenGroups/Pages/IntroFungi.aspx