Experimental data up to now have established that the underlying level of nature is quantum mechanical, i.e. described by the theory of quantum mechanic.s. This theory makes accurate predictions for dimensions commensurate with h_bar
Classical mechanics describes set ups where h_bar, whose value is of order 10^-34 joulesecond , is essentially zero due to its tiny value.
As a conceptual example take Thermodynamics, which is an elegant and complete theory describing the macroscopic behavior of bulk matter. It has been shown that it emerges from the underlying framework of particles , from statistical mechanics exploring smaller dimensions than the macroscopic where thermodynamics holds, in a consistent mathematically manner.
In a similar way it can be shown that classical fields emerge from the underlying quantum mechanical framework.
Classical many body objects, like this screen, have a collective state function described with a huge number of variables. The density matrix formalism is used to describe the transition from a few body quantum mechanical system where effects of QM are measurable to a classical system.
A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single state vector that describes a quantum system in a pure state. The density matrix is the quantum-mechanical analogue to a phase-space probability measure (probability distribution of position and momentum) in classical statistical mechanics.
The quantum mechanical form:
For a system of many quantum mechanical bodies, an operator in matrix form. When dimensions are such that the off diagonal elements are essentially zero ( due to h_bar value) one is describing a classical system.
Are classical objects considered to be a collapsed wavefunction of the system or the subsystems or what?.
The "collapsed" language is not useful here, there is nothing sudden (collapse) there is just large dimensions and large numbers that create the emergence of classical from quantum. It means that the influence on probabilities of molecule 1 on molecule n is so small it can be considered zero when describing a classical object.