I assume you paid them for demolition? I would read the fine print in their contract and see if it allows for them to move. If they are going to make use of it, seems like you should be compensated.

Did you want the existing structure removed from your property? Do you care how it was removed?

That said, I think I'd have a discussion with the demolition company to find out what happened and how.

Just ask the demo company how this came to be.

Here's what I'll bet happened: the neighbor heard you were having the existing structure demolished. Neighbor was home when the demo company arrived and walked over to ask if they could have this piece and offered to pay cash for it to be shoved over on their property.

OR, the neighbor is related to or friends with the demo company and actively pursued this with them without your knowledge. Maybe Joe the demo guy is a brother to Moe, your neighbor.

OR, the demo company has a system in place whereby they notify interested parties when they will have a salvageable building available.

I'm always excited to see my houses, some of which I've lived in and renovated for years, turn to rubble before my very eyes.

Still, I wouldn't feel cheated if instead the home were hauled away for someone else to enjoy. (But I'm not you.)

Finally, a story to beat Mike's aka Trashcanman's tale.

You paid for them to remove the cottage from your property. They did. Job complete.

Why would it matter that your 'garbage' ended up somewhere else instead of the dump? If you put a couch out on the curb for the garbage truck to pick up, would you care if someone else came along and took it first? This is the same situation, except on a bigger scale.

"...Finally, a story to beat Mike's aka Trashcanman's tale..."

OMG...what if these were the same neighbors? Hide the dog and pet pig...

Just checking: the neighbors are good with this? If the demo guys didn't realize that they put it on someone else's property that could be an issue.

I'd also be glad if it's being reused rather than junked, but Mark makes a good point about liability.

I would check to find out what happened and make sure you'll not have any liability. Otherwise be glad that your lot is cleared and especially that the buildings are being reused instead of clogging the landfills. Maybe have your neighbor over for some wine & cheese to celebrate their reuse.