LSMFT wrote:
If I survey my property line and dig a ditch around my property up to
that line, am I responsible for my neighbors land sliding into my ditch?

You might need permission from the local government officials. It
doesn't take much for a draw to be called a stream.
A local farmer wanted to do some work to his farm to run an
irrigation system. I think even the Army Corps of Engineers got
involved. This draw was dry most of the time. It had running water in
the spring during the snow melt and maybe sometimes after a heavy rain.
Another problem might be if your land is called a wetland. Has a
duck landed there in the last 5000 years or so? I'd suggest doing a
little checking before you start.