How do ships catch fairings? Can fairings steer or do the ships do all the work?

A comment in The Pod Bay says it all:

…fourth Starlink payload launched. Booster landed on OCISLY. (Has now launched three times, LC-39A, SLC-40, SLC-4W once at each launch pad they own!)

And they caught a fairing in a boat with a net. Seriously, can you make this stuff up? emphasis added

I'm guessing the net is not much larger than 10 meters on a side, and fairings generally separate above 100,000 meters, moving quite fast (except when it's even higher).

SpaceX fairings appear to use cold gas thrusters early in their descent, but at some point they will enter the atmosphere and descend through layers with different wind speeds and directions, and at some further point they will deploy parachutes.

Question: Do SpaceX fairings have any control over their descent once in the atmosphere, or is all maneuvering for interception done by the ship?

click for full size, images from 2018

left: from this question and SpaceX tweet, right: from this answer and Pauline Aclin, Teslarati 7th May 2018