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Was wondering if you take a small branch from a fruit tree and dip it in rooting hormone and are successful in propagating it, will the resulting tree will be a true representative of the original tree?

I know that if you plant a seed, you never know what you'll get, and if a tree comes up from the roots you'll only get the rootstock on which it was planted. But, I'm thinking if you propagate a branch from the tree, it will be the same as the tree? But, since it's not on rootstock, it will just grow as a standard sized tree?

I have some branches like that from an apple and a pear that seem to be leafing out in buckets. I'm not sure if they'll make it or not, but was hoping they will be the same as the original trees! I just did it for fun, it seemed to be a shame to throw away the pruning twiglets so I thought I try to propagate some!

Some trees will grow from cuttings. I have grown Meyer lemon and Bearrs limes from cuttings. Some will grow but are a little harder to start. I think anything that will air layer will probably grow from a cutting taken at the right time.

If you propagate cuttings from a tree then it will grow true to that trees variety. That's the way all trees are propagated....either by scion ( a small shoot ) or by bud grafting.
The actual size of the tree once it's grown is anyone guess though. Tight root control or growth by pruning will give some control but unless it's grafted onto a known rootstock it's a bit hit and miss.

Thank you. So, the tree will not necessarily go to the large standard size then?

That's the big guessing game Taiiji when you propagate by rooting scions.
There's no way of knowing what they will grow like. If we did it would make planting an orchard a whole lot cheaper!

hmm I see. I guess I thought that any root system from a tree branch would just automatically be standard. Whereas dwarf and semi dwarf root systems were human invented.

We know that the Persians perfected grafting some 10000 years ago and by the time the Romans 'borrowed ' the skill from them there was at least some form of root stocks known.
Even so..the trees in their orchards must have gone up and down a bit.
The EMLA/ MM stocks of modern times made huge jumps in tree control.