Uncountable superperfect forcing and minimality

Uncountable superperfect forcing is tree forcing on regular uncountable cardinals κ with κ < κ = κ , using trees in which the heights of nodes that split along any branch in the tree form a club set, and such that any node in the tree with more than one immediate extension has measure-one-many extensions, where the measure is relative to some κ -complete, nonprincipal normal filter (or p-filter) F . This forcing adds a generic of minimal degree if and only if F is κ -saturated.