The computation of a nondeterministic Turing machine (NTM) is well known to be representable as a tree of configurations, rooted at the starting configuration. Any transition in the program is represented by a father-child link in this tree.
Similar trees can also be constructed for visualising the computations of probabilistic and quantum machines as well. (Note that it is better for some purposes not to view the related graph for quantum computations as a tree, since two nodes representing identical configurations at the same level of the tree can "cancel" each other out, due to quantum interference, but this doesn't have anything to do with the present question.)
Of course, deterministic computations are not like that; there is a single "branch" in the corresponding "tree" for any run of a deterministic machine.
In all the three cases mentioned above, what sometimes makes these computations "difficult" for deterministic computers is not really that there is branching going on, rather, it is a matter of how much branching is present in the tree. For instance, a polynomial-time nondeterministic Turing machine which is guaranteed to produce computation trees whose "widths" (i.e. number of nodes in the most crowded level) are also bounded above by a polynomial function of the input size can be simulated by a polynomial-time deterministic TM. (Note that this "polynomial width" condition is equivalent to restricting the NTM to make at most a logarithmically bounded number of nondeterministic guesses.) The same thing is true when we put similar width bounds on probabilistic and quantum computations.
I know that this issue has been examined in detail for nondeterministic computations. See, for example, the survey "Limited Nondeterminism" by Goldsmith, Levy, and Mundhenk. My question is, has this phenomenon of "limited branching" or "limited width" been studied in a common framework encompassing all of the nondeterministic, probabilistic, and quantum models? If so, what is the standard name for it? Any links to resources will be appreciated.