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Local models are schemes, defined in terms of linear-algebraic moduli problems, which are used to model the étale-local structure of integral models of certain 
$p$ -adic PEL Shimura varieties defined by Rapoport and Zink. In the case of a unitary similitude group whose localization at 
${ \mathbb{Q} }_{p} $ is ramified, quasi-split 
$G{U}_{n} $ , Pappas has observed that the original local models are typically not flat, and he and Rapoport have introduced new conditions to the original moduli problem which they conjecture to yield a flat scheme. In a previous paper, we proved that their new local models are topologically flat when 
$n$ is odd. In the present paper, we prove topological flatness when 
$n$ is even. Along the way, we characterize the 
$\mu $ -admissible set for certain cocharacters 
$\mu $ in types 
$B$ and 
$D$ , and we show that for these cocharacters admissibility can be characterized in a vertexwise way, confirming a conjecture of Pappas and Rapoport.
