Ditto what jedobaTX said. All kinds of cultivars grow in all sizes. The major online nurseries in the US try to provide size at maturity which is helpful when planning location.

However, I am not sure what cultivar mine is. Does this matter on the growth and appearance of the plant?

It may grow that fast every year! I have one that grew 4 feet in ground this year, and bloomed three times! Most of my others got one or two blooming cycles, and nowhere near the height.

If you have it potted, it will reach a maximum that the pot will allow the roots to grow, and that will limit the tree.

The nubs you see are new branches!

When they do get branches, does it normally have an inflo on each branch? Will it put out branches with each inflo? If so, is this number consistent?

Yes, you will eventually get inflos on each branch. Also, each time you get an inflo, it will cause it to branch.

We can only hope it will stay consistent.

Plumeria cultivars differ in how much they grow before they bloom. For example, my 'Divine' may only grow three inches before it puts out a new bloomstalk (inflo).

On the other hand, my 'Vera Cruz Rose' can easily grow four feet or more before it blooms.

It sounds to me like you have one that is just going to grow tall and vigorously. So at three feet, it's really just a baby. But once they develop multiple growing tips, and get some size to them, they do slow down just a bit.

It should branch at the inflo.

If it flowers every year, it might branch well without interference. If it doesn't, you might want to consider pruning it, especially when you have to drag it in for the winter. The more compact you can get it, the easier it is to handle, and the more flowers it will have.

They are decent sized trees in the wild, so they try to branch less frequently and can end up looking really leggy and bare. They'd fill out in the wild eventually, but they don't have enough space in a pot.

So the cultivar does not matter too much? Should I expect yearly blooms/branching?

If they're happy, they'll bloom every year. Nutrition issues and pests will sometimes stop them from blooming.

You can also prune during winter so you don't accidentally abort the entire bloom cycle

Cultivar will have some impact on size or branching, but since it isn't a dwarf variety, it shouldn't vary a ton.

Plumerias are mostly grown for their flowers, so traits like branching and growth rate aren't really taken into consideration unless it produces results faster.

So, cultivar might have some impact, but I doubt someone has actually gone to the trouble of comparing cultivars growth rate.

Nutrition, health, and temperature are going to have more of an impact than anything else. Even if it had super genes, it's not going to grow well if it doesn't have the right growing conditions.

It's been my experience a healthy plant initially grows fast and then after about 5-7 years begin to slow down. You can see this in the leaf scars and how spread out they are on the lower parts of the plant and as you get further up into the canopy you see the scars much closer together.

It also depends on whether you are growing from a cutting or from seed. And what part of the world you are growing these. And whether in-ground or in a pot.

All three are cutting, it is in Northeast NJ and is in a pot, if that helps.

Yes, it's helpful to know the culture of the plant. For example, in mild climates where they can be grown outdoors year-round in full sun, plants tend to be more compact - especially in dry climates. But when we have to pot them up, and move them inside, they tend to get leggier before they bloom and branch out. At least that has been my observation.

Ive seen 2 pink ones grown like trees, at least 2.5 stories tall that were shading a whole small backyard, maybe 30’ x 30’ wide. The Waxy leaves killed of all vegetation below them, but was perfect for a table and grilling spot. It was beautiful. Heres the tall plumeria photo ive found so far. The one I saw was taller By maybe 5-8’.