I believe you will find that the tree belongs to you. Of course, I am unsure what your neighbor gets out of "co-owning" a tree. The fact that some roots may extend under the neighbor's land technically, I suppose, involves some trespass on their land, but given there is no loss to them it should be a non issue. There may be case law or a statute that even addresses such an issue.
I am hopeful that a WA lawyer with experience in this area will address the question, as it is an interesting one.
Parenthetically, there really is no way for the neighbor to gain ownership in the tree, at least under traditional common law doctrines. He cannot adversely possess it nor gain a prescriptive easement for it.
I agree with the previous answer and the problem usually involves removal, cost or preservation of the tree. If you remove the tree because of liability, view, aesthetics , or for development then your duty was to survey which you have done. Now the question of what is next? That will depend on your goals. You may without liability trim what is directly over your property line, as long as the tree lives afterward. If you remove the tree and you neighbor claims damage he has to prove the amount of damage and he may be awarded attorney fees , ( the worst part) and treble damages if it was intentional.
I would suggest a long talk about your goals with your neighbor and your attorney not necessarily in that order.
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The question may not be capable of a definitive answer under existing Washington jurisprudence. Remarkably, despite how commonplace this situation likely is, the law is not well developed in this area. In particular, this factual scenario appears to involve the intersection of two different legal principles.
First, as indicated by others in this post, it is generally recognized that a property owner may, in most circumstances, cut encroaching branches and roots (only up to the property line) from trees originating from the adjoining owner’s property. In other words, your neighbor could likely trim the branches and roots of the tree, and there would likely be no legal recourse.
Second, one of the three intermediate appellate courts in Washington has held that “a tree, standing directly upon the line between adjoining owners, so that the line passes through it, is the common property of both parties, whether marked or not; and trespass will lie if one cuts and destroys it without the consent of the other.” See Happy Bunch, LLC v. Grandview North, LLC, 142 Wn. App. 81, 93 (2007). In its holding, the Court expressly rejected the argument that “absent a showing of an agreement to the contrary, a boundary line tree belongs entirely to the party on whose land the tree was originally planted, with damages calculated accordingly.” In other words, the fact that your tree was originally planted on your property may not be determinative of whether you own it in its entirety under Washington law.
Critically, the Happy Bunch court did not define “tree.” However, in light of the first principle above, the Court was likely referring to the trunk of the tree, because cutting overhanging limbs and roots is generally recognized as lawful. Ultimately, the Court awarded damages to the plaintiffs, because the defendant did cut trees that were “common property” (i.e., straddling the property line). However, the damages were pro-rated based upon the percentage of the trunks on the plaintiff’s property prior to cutting. Interestingly for your purposes, the damages in that case were based upon the “Trunk Formula Method,” which arborists typically use to value trees, with the diameter of the tree being measured at diameter breast height (DBH), which is usually several feet above ground level, with the purpose of measuring above any taper or flair to the tree.
The bottom line is that you should tread carefully. As indicated by others, you could be liable for treble damages, and even attorneys fees or other costs, if the tree is considered “common property” and it was removed without your neighbor’s consent. See RCW 64.12.030; RCW 4.24.630. However, even if the tree is common property, and you elected to remove it, and your neighbor decided to pursue the matter, a court might only award damages in proportion to the percentage of the tree on your neighbor’s property. Based upon your description, it sounds like little to none of the tree would be on the neighbor’s property, depending upon whether the trunk is measured at DBH or at the root taper. Also, if you do decide to remove the tree, you would need to do so without creating other damage to your neighbor’s property. In this case, stump removal would likely be a bad idea. Finally, it is also possible that if your neighbor’s conduct kills your real estate transaction, you might have claims 1) to establish ownership of the tree, and/or 2) for tortious interference with the transaction.
This answer is provided for informational purposes only and should not be relied upon or construed as legal advice or legal opinion. The answer is based upon limited facts and general principles of law, both of which are subject to change and, therefore, may materially affect any answer given. You should contact an attorney to obtain advice with respect to your particular issue or problem. This answer does not create an attorney-client relationship, nor does it create any kind of legal relationship, duty, or privilege. This attorney is licensed only in the State of Washington.