What are the 't Hooft papers about classical models underlying QM? Gerard 't Hooft states on his webpage:

I have mathematically sound equations that show how classical models generate quantum mechanics.

Also, there are some interesting discussions here on Physics SE about the question, see for example Discreteness and determinism in superstrings and Deterministic quantum mechanics [or searching for "+hooft +determini*"] and the links therein.
Which of the 't Hooft papers in arXiv should I read in order to grasp the question? Could anybody provide an ordered list? I would like to restrict myself for the moment to those strictly related to quantum mechanics, to grasp the ideas within a known framework. (I have seen that the question extends to the realm of string theory, where I am for the moment nearly ignorant.) 
 A: Well since this is a request for  a reference to a paper one need not be a theorist.
I would start with the last reference 't Hooft himself gives in the paper found in the link at Physics SE. The last reference there is on the non-string model: "The mathematical basis for deterministic quantum mechanics" (arXiv:quant-ph/0604008).
Abstract:

If there exists a classical, i.e. deterministic theory underlying quantum mechanics, an explanation must be found of the fact that the Hamiltonian, which is defined to be the operator that generates evolution in time, is bounded from below. The mechanism that can produce exactly such a constraint is identified in this paper. It is the fact that not all classical data are registered in the quantum description. Large sets of values of these data are assumed to be indistinguishable, forming equivalence classes. It is argued that this should be attributed to information loss, such as what one might suspect to happen during the formation and annihilation of virtual black holes.
The nature of the equivalence classes is further elucidated, as it follows from the positivity of the Hamiltonian. Our world is assumed to consist of a very large number of subsystems that may be regarded as approximately independent, or weakly interacting with one another. As long as two (or more) sectors of our world are treated as being independent, they all must be demanded to be restricted to positive energy states only. What follows from these considerations is a unique definition of energy in the quantum system in terms of the periodicity of the limit cycles of the deterministic model.

You could then follow backwards in time the references of this one.
