Beginner Gardening: Why is my aloe pup still a "pup"?, 1 by MTGardenGirl

MTGardenGirl wrote:
I was in the military for many years and in 2008, I was jogging one morning in a remote area on the base I was stationed at in San Antonio. I came across a clump of Purple Heart that was growing under a Pecan tree in the middle of a field...I stopped to check it out and hidden in the giant purple foliage was what appeared to be a small Aloe plant. I cleared some of the growth away and I found a huge woody root (?) covered in Aloe. The plants were about 2-3 feet in diameter and about 2 feet tall, it was so awesome. I think the wood part that they appeared to be growing on was actually part of an old mother plant. So, I picked off a small pup that was about 2-3 inches tall, with 3 stalks. I planned to go back and take more of the plant, but the base started construction the next day and I had no access to the tree. I potted the pup and placed it in a sunny, south facing window. It was slow going, but it didn't die- I was super happy with that. Well, I moved to Montana about a month later and brought my pup with me. It has been 2 years now, I've repotted him once and he seems to be growing, but I'm suprised that this plant doesn't seem to be growing in a rosette. I had many rosette-style Aloe growing in my front yard in TX and I assumed that once this new pup got started that it would take the shape I was used to seeing. As you can see in the picture, it has grown quite a bit, it is about 10 inches tall and has new growth. I have it in a 4" terra cotta pot in a southeast, bright sunny window. My question is: how long will it take for this plant to get to a mature-ish state? I almost feel like I should start staking it, it has become very wobbly and top heavy (suprising, since it's still pretty small). Does anyone know what type of Aloe it is? It seems very common, but I've never seen any grow straight up and down like this. Please ignore the burns on the leaves, my 10 year-old daughter was trying to "help" a few weeks ago and took it outside and left it in direct sun at the hottest part of the day for a few hours :-) Thanks!