With few exceptions, the "plants" we put in reef tanks are not plants, but rather macroalgae. Some of the most common varieties are chaetomorpha (chaeto for short), caleurpa, gracilliara, and halimeda.
It's actually possible to do a lushly plants marine tank. My refugium is very heavily planted and is fun to observe in it's own right!
Couple things to note with macro in the display tank.
One, they will absorbs nitrate and phosphate and store the components in their tissue. As they grow, you trim and remove portions. When you remove a chunk of caleurpa, you are exporting the excess nutrients that the caleurpa has collected. Hence, nutrient export. The algae themselves simply perform nutrient uptake. Which brings me to the next point.
If certain macro algae are not trimmed periodically, they have a tendency to cease asexual reproduction (runners, shoots, and just general spreading) and begin sexual reproduction by releasing primitive gametes, or spores.
When a macro algae sexual event occurs, the parent algae dies and releases all of it's stored nutrients back into the water.
So, if a chunk of caleurpa has been collecting nitrate and phosphate for 6 months, goes sexual and dies, in addition to spores all over and the caluerpa taking over the tank, it has just dumped 6 months worth of nutrients into the tank over night.
You can recognize sexual events before they occur, however. Caleurpa turns white. Halimeda becomes fuzzy. Just research the type of algae. I don't think Chaeto has a sexual event.
Anywho, I happen to love macro algae and collect it. I have Caleurpa (three varieties), Chaeto, Halymenia, Halimeda, Mermaid's fan, shaving brush, and pinecone.
Someone stop me! Please! But... not just yet...
55 Gal Tropical FW
55 Gal Mixed Reef