"I have had part of an oak fall from the neighbors property onto mine. The oak stradles the property line so I figure what fell on my property is mine."
This is a bit ambiguous, but I think you are saying that the tree was on his property and fell across the bounrdy between the two properties. You want what landed on your property. If that is the case, then I don't think it is your tree at all. The way I see it, if the tree fell from his property onto yours and damaged your fence, shed, house, or car, etc, he would be responsible for the damage. Even if there is no damage, he is responsible to clean up the debris and should clear it with you first before he or any workman go onto your property. With that the case, I think the wood is his if he wants it.
Having said that, I agree with the others who suggested that youu talk to him first, unless you already have a poor relationshiop with your neighbour. For all you know he may not want the wood and may give yo the whole tree. Or maybe he will just want the branches for firewood and will give the trunk to you because it is too large to chunk up and split anyway. WIth all of my neighbours the first thing we would have done was take a walk out to the tree and chew the fat while we consider what to do next.
