Who owns this tree?

[BentFork]

20yrs ago my neighbour planted a skinny sapling touching the fence she owns that divides our properties. It literally was a twig back then. Over the years the fence bowed my way as the tree grew. I ignored this as I was busy with life, although the fence bending in did nark me a bit. Now new neighbours have moved in and had the garden refurbished, including all new fencing. The tree is so mature if you hugged it, your arms barely go halfway round the trunk. The new fencing had to be sliced to accommodate the tree as it now sits 75% in my garden. With the old fence so dilapidated, neither of us realised quite how far the tree had moved.
To top it off, the neighbour has now had the tree sliced level with the top of the fence. So all that remains is a large bald trunk. They had quotes to remove it so they could have a perfect run of fence but it was 12k, so they left it & just cut the top off.

Is this tree still my neighbours sole property?

We need a diagram.

If it was overhanging your property (but trunk was next door) it would belong to your neighbours. (You can lop branches off if you like but are supposed to return them to the owner if you do!) But if it's effectively growing right in the middle of the boundary I can't see how who planted it really matters as it's presumably shared? £12k seems to lot to deal with a tree. I'd just let to regrow (effectively having pollarded it) or else treat the top of it to kill it and stop it regrowing. If you do that, it will eventually die and rot away, though may take another 20 years.

It would have cost a tiny percentage of £12k to remove, op.
That wasn't the reason they kept it.

"They had quotes to remove it so they could have a perfect run of fence but it was 12k, so they left it & just cut the top off."

Absolute rubbish. To grind a tree stump of that sort of size (assuming maybe 120cm in diameter?) you're probably talking £400-£500 at most.

By grinding a tree stump I mean taking it down to below ground level. If they have already removed the tree from above the height of the fence then how high is the fence - maximum of 2 metres. To remove a 2m trunk and grind the stump really is not going to be more than £500.

Not sure why you are asking the question? I would assume as your ex neighbour planted it on their property the ownership of the tree would pass to the new owners. Only a conveyancing solicitor will be able to give you a definitive answer.

No way that would cost £12k. A family member had a quote for a huge Eucalyptus that spanned 3 neighbours gardens recently (they live in a wood so there is a canopy of trees above their gardens) and it was cheaper than that to remove.

Christ Almighty, why do people butcher trees like this?

Despicable bastards.

We had a similar situation with a tree that appeared to be in our side of the boundary but was damaging the neighbours fence.
We agreed with he neighbour to take our down.

The tree wasn't a big add you are describing, but whoever quoted 12k was not being serious (unless you've missed something from this scenario).
Your neighbour has already done the expensive part of removing a tree by having the top taken down.
Taking the tree to ground level and getting a stump grinder to remove the rest is relatively cheap. As others have said, a few hundred pounds.
It sounds like this will be in your interest too, so why don't you offer to get an alternative quote and go halves?