Shared hedge (cotoneaster)

in Plants
Hi, I've got a shared hedge with some new very lazy neighbours. They have suggested that they may want to block path their drive (there is a rose garden currently there) - question is if they do this in the summer is there a chance that it may kill the hedge? It grows on both sides of the property but there is only me who tends to it. There are also lots of house sparrows who nest in the hedge.
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"We don't stop playing because we grow old; we grow old because we stop playing." - George Bernard Shaw
That said, legally you need to know where your boundary is. Once you are sure of your boundary then both of you have the right to cut right up to the boundary, and for one of you that will mean the trunk as well. So to put it bluntly, if the point at which the plant meets the ground is on his side of the boundary, he can dig up the plants anyway and you have no say in the matter. And vice versa. In fact if you cut the plants you are obliged to offer him the cuttings (if the plants were to turn out to be on his side of the boundary), and if refused, disposal is at your expense - but very few people bother with this.
I suspect they have different priorities in life to you. Do you know the ins and outs of their life inside their home?
They can do whatever they want on their side of the boundary, hedge roots or not. It's none of your business to be frank.
Sometimes the honest replies on this group get people wound up! Look at it as a balanced viewpoint and it may help you work out the best approach.
This could be a dictionary example of xenophobia