The short answer
No, do not throw them back.
The longer answer is more interesting, because the reason is not really the law. It is that the branches over your fence are almost never worth the relationship.
Whose branches are they
The traditional common law position is that severing an encroaching branch does not make it yours. The material remains the property of the tree owner, along with any fruit attached to it. The same applies to roots you cut on your side of the boundary.
That surprises people, since you are the one who paid to cut it. But the right of abatement is a right to stop the encroachment, not a right to acquire the thing encroaching — the full framework is in whose responsibility overhanging branches are.
Why throwing it over is a bad idea
It may be trespass. Depositing material on someone else's land without permission is not something you have a right to do, even if the material originated there.
It can be a hazard. A pile of branches dropped over a fence into a yard where there are children, a dog, a pool fence or a driveway is a problem you created, and if it causes harm or damage the fact that it grew on their tree is not much of a defence.
It escalates. Every neighbour tree dispute that ends up in front of a mediator or the Land and Environment Court has a moment where it stopped being about the tree. A ute-load of prunings dumped over the fence is very often that moment.
What to do instead
Offer them back. Ring, knock, or send a text. "I've cut back the branches over my side — do you want the material, or shall I get rid of it?" Almost everybody says get rid of it. You have now behaved correctly and you have a record of it.
Dispose of it properly. Green waste bin for small material. Council green waste drop-off for larger loads — all three councils in this region take it. For anything substantial, the crew doing the pruning chips it on site and takes it away as part of the job, which is the reason most people do not do this themselves.
Get it in writing if there is any tension. A short text confirming what you cut, when, and what you offered takes ten seconds and is worth a great deal if it ever becomes a dispute.
Do not cut it in the first place if you are angry
The practical advice at the heart of all of this: an overhanging branch is a cheap problem and a bad neighbour relationship is an expensive one. Before you cut anything, read how to approach the conversation, and before you cut it badly, read how to make the cut.
Splitting the cost of a proper crown reduction generally costs each of you less than either of you spends on a dispute, and it leaves the tree in better shape than either abatement or argument.
If the tree is council's
Different situation entirely, and the rules are stricter. See council trees overhanging private property and trimming council trees.
For a quote on boundary work including green waste removal, ring (02) 4210 5885.
Frequently asked questions
Is throwing branches back over the fence illegal?
Throwing material onto someone else's land without permission can amount to trespass, and depending on what lands and where, it can also create a nuisance or a hazard. It is rarely worth anyone prosecuting, but it is the wrong side of the line and it reliably turns a small tree problem into a long-running neighbour problem. Offer the material back instead of hurling it.
Who owns the branches I cut off an overhanging tree?
The tree owner. Cutting an encroaching branch does not transfer ownership of it to you — the traditional position is that the severed material, and any fruit on it, remains the property of the person who owns the tree. In practice most neighbours do not want a pile of prunings back, which is why offering first and then disposing of it is the workable answer.
Can I keep the fruit from a branch hanging over my fence?
Strictly, no. Fruit growing on a neighbour's tree belongs to the neighbour even where the branch it grows on hangs over your land. Nobody has ever gone to court over a lemon, and most neighbours will tell you to help yourself if you ask. But the legal position is worth knowing before you strip a fully laden branch over the fence line.