You're looking for coral that are typically called "Stags" (short for Staghorn), though some Stags are more vertical than others. Here are the ones that first come to mind when I think of vertical Stags that hit the water surface first. :lol:
Acropora yongei - easy species. Typical "Green Slimer", other color varieties
Acropora exquisita - a bit more challenging, but doable for most
Acropora hoeksemai - typically a challenging coral, many experienced keepers have trouble with this one, but get the right conditions and it takes right off
There are several others, but these are the three that hit the water surface first for me.![]()
Ah, well now you're asking for something totally different...I have to add I'm not a big fan of long horned style stags. Green slimers are one of the ones that seem to look exactly like deer antlers and get long. I would love a compact style of antler. branching and vertical but smaller.
birdsnests (especially the pink ones) seeem to grow like weeds. I grew mine from a 1.5" frag into just slightly smaller than a soccer ball in 2 years. You can see growth every day on those, but they arent exactly vertical. They grow out in all directions and very dense.
Torts are a bit less "horn" like, but they are not fast growers.
Montipora Digitata are very very fast growers and have a semi vertical appearance. My avatar is one example. It was my pink digi..that damn thing grew like a weed!