The three rules that settle most disputes: (1) If a healthy tree falls in a storm, each owner's insurance handles damage on their own side — storms are "acts of God" and nobody is at fault. (2) You may trim branches that cross your property line, at your own cost, up to the line — but not in a way that kills the tree. (3) The exception that changes everything: a visibly dead or dying tree the owner ignored can make that owner liable when it falls.
The neighbor's tree fell on my fence — who pays?
Your fence, your insurance claim — even though it was their tree. That feels backwards, but it's how Texas (and most states) treat storm-felled healthy trees. Your insurer may pursue theirs if negligence applies. Practical move: photograph the fallen tree including the trunk condition before cleanup, so rot or beetle-kill is documented.
The dead-pine exception (very Walker County)
East Texas is full of standing beetle-killed pines from the freeze-and-drought years. If your neighbor's pine is obviously dead and leaning your way, put your concern in writing (text works, certified letter is better) — that paper trail is what turns "act of God" into their liability if it falls. And if it's your dead pine: a removal costs less than your deductible plus the argument.
Can I trim what hangs over my side?
Yes — Texas common law lets you cut back to the property line at your cost. Two cautions: you can't enter their property without permission, and butchering an oak (or cutting it in the Feb–June oak wilt window) in a way that kills it can make you liable for the tree's value. Clean, correctly-timed line trims are exactly the kind of job worth not doing off a ladder yourself.
Whose tree is it when the trunk straddles the line?
Shared property. Neither owner may remove it without the other's consent. Get agreements in writing — a one-paragraph text thread has settled more fence-line trees than any lawyer.