About the turing machine's non-deterministic branches I have three different cases of non-deterministic turing machine.
The first machine has:
Branch "accept" and branch "loop".
The second has:
Branch "rejecte" &amp; branch "loop".
Third has:
Three branchs "rejecte" "loop" "accept".
The question is which machines will  rejecte and which ones will accept and which ones will enter a loop?
Thank you so much
I guess, with branches you mean the computation branches (the sequence of the konfigurations M has in its computation) of $M$. Then in general a NTM $M$ will accept an input x, if there exists one computation branch in the computation tree, which leads to accept x, no matter, where other branches may lead to (even if there infinite long). So, Machine 1 and 3 will accept. 

I am definitely not sure about the following: I guess, the question, what Machine 2 will do is not decidable (please correct me, if I am wrong)