In single player I imported a planet sector in a black hole system to see what would happen. The planet was 3 sectors away from a black hole, and didn't seem to be affected by the black hole's gravity (no surprise there). However, any attempts to land on the planet were mixed at best.
In a 3-block scout ship (core - power - thruster), the ship couldn't figure out which thing had the bigger pull on it, so I got out to see what would happen. At that point, the the black hole's gravity won out and I watched my ship fly away, slowly at first, then faster until it was out of sight. It was as poetic as it was disappointing. I tried again with another ship, on the side of the planet opposite the black hole. Once I got out, the ship was pulled into the planet's surface, glitching through, until it also succumbed to the black hole's gravity.
I don't know if there's a lesson to be learned here. Gravity...sucks?