  Local models are schemes, defined in terms of linear-algebraic moduli
problems, which give \'etale-local neighborhoods 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 Q_p is ramified, quasi-split
GU_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.
