How to fix black 'veining' around drain hole of vanity sink?

That is a problem with cultured marble sinks. Cracks form around the drains. Try a paste if baking soda and hydrogen peroxide. Slather it on a dry sink and let it sit till it dries. Then rinse. They will come back. Sometimes it's the veining process in the manufacturing.

Try using Bar Keepers Friend. Wet the sink, then sprinkle on, let it sit for about an hour. Scrub clean.

I will be surprised if this comes off with scrubbing. I have found when small cracks form and dirt finds its way down those cracks it does not lift up out of the cracks.

Good Luck, would love to know if you find something that works. So far I have not.

Mine has done this, too. Have found that spray on gel bleach makes it better for a time. Have considered refinishing the sink bowl with a tub and tile epoxy paint. Has anybody tried this?

You may try painting it before replacing

https://www.hometalk.com/search/posts?filter=paint%20bathroom%20sink

Comet

A lot of that is caused from using bleach-type products, sad to say. I use denture tabs, left overnight. Just pick some up from Dollar Tree, over time it really diminished the stains.

I would seriously consider painting it since nothing seems to touch it. Just a suggestion, call the manufacturer and see what they suggest.

Have you tried denture tablets? That may help.

I would make a paste of bleach and baking soda. The baking soda is really only there to hold the bleach in place like a thick paste. Let it sit over night and then remove the excess and wipe the area clean using a clean cloth and fresh water.

Try Toilet Bowl Cleaner Lysol 10x, Blue Bottle. Test Area, 10 minutes. If it works, then try the whole Area.