Super McDuff and Uniformly Super McDuff II₁ factor

In this paper, we prove that every super McDuff II₁ factor is uniformly super McDuff. In particular, the classes of super McDuff and uniformly super McDuff II₁ factors coincide. This answers [Question D]{GJKEP} affirmatively. For factors with separable predual, super McDuffness is therefore equivalent to the Brown property and is preserved under elementary equivalence, also answering [Question~6.2.1]{AGK22} affirmatively. We further show that every infinite tensor product of non-$Γ$ II₁ factors is uniformly super McDuff. For a finite tensor product of separable II₁ factors that is super McDuff, each tensor factor is either non-$Γ$ or uniformly super McDuff, and at least one is uniformly super McDuff.