  We study the scalar sector of the most general multi Higgs doublet model
satisfying explicitly an exact symmetry. We prove that such a model will
exhibit decoupling if and only if the vacuum also satisfies the same symmetry.
This general property is also shown independently and explicitly for three
Higgs doublet models, by considering in detail all symmetry-constrained models
and their possible vacua. We also discuss some specific characteristics of
different decoupling patterns.
