Dependence of decoherence-assisted classicality on the way a system is partitioned into subsystems

Choosing a specific way of dividing a closed system into parts is a starting point for the decoherence program and for the quantum thermalization program. It is shown that one can always choose a way of partitioning so that decoherence-assisted classicality does not emerge and thermalization does not occur. Implications of this result are discussed.