Hmmm, can I ask why you would want to propagate a plant that is environmentally damaging in your part of the country? Albizia julibrissin is invasive and probably best avoided.

Peach trees (at least edible and ornamental cultivars) are usually propagated by grafting scions onto compatible rootstock. If you're just wanting to grow something and don't care about the fruit or how the tree looks, it's easy to grow pretty much any prunus species from seed.

My son planted a mimosa close by his house and it grew rapidly. His was a modern concrete slab construction house and soon he noticed the floor buckling up. The first year he took out the tree, the next year he tunneled under the slab to kill the root which just kept on growing. That is a bad news tree. Al

Hi & welcome to Gardenweb. Love the sentiment in your profile.

You may want to ask about the peach on the tree or fruit & orchards forums. You'll get a lot more responses without mimosa anecdotes.

Propagating the mimosa should be no problem, if you're determined to do so. As said above, they're extremely determined to grow.

When I moved here 5 years ago, there was a stump enmeshed in the chain link fence that had obviously been the victim of attempted murder many times. The first two years, I made nominal attempts at "keeping it cut back." It really liked it. The third year, I started killing it about weekly. That made it start to think about getting nervous. Last year, I started killing it every day, rubbing and scratching off any visible growth, buried as much as I could under a pile of leaves, hacked at the stump, dug up roots, and said some really ugly things to it. It got mad. This year, I started earlier, have not missed many days, dug more roots, put potted plants to make shade on it. It still grows new green "bumps" every day, but they may be smaller (or just wishful eyesight.) At this rate, I think it may actually die in a few more years.

So it's hard to imagine that any branch or twig stuck in the ground wouldn't immediately seize the opportunity to grow and proliferate itself for miles around. Which brings us to the seeds, which are plentiful and sprout easily, another option for propagation.

But, as Brandon said, this species is a Category C invasive in Missouri. PCA also has a thorough article about Albizia julibrissin. They are pretty though, aren't they? I try to enjoy the millions I see driving around instead of letting one grow in the yard.