  We prove a representation for the support of McKean Vlasov Equations. To do
so, we construct functional quantizations for the law of Brownian motion as a
measure over the (non-reflexive) Banach space of H\"older continuous paths. By
solving optimal Karhunen Lo\`eve expansions and exploiting the compact
embedding of Gaussian measures, we obtain a sequence of deterministic finite
supported measures that converge to the law of a Brownian motion with explicit
rate. We show the approximation sequence is near optimal with very favourable
integrability properties and prove these approximations remain true when the
paths are enhanced to rough paths. These results are of independent interest.
  The functional quantization results then yield a novel way to build
deterministic, finite supported measures that approximate the law of the McKean
Vlasov Equation driven by the Brownian motion which crucially avoid the use of
random empirical distributions. These are then used to solve an approximate
skeleton process that characterises the support of the McKean Vlasov Equation.
  We give explicit rates of convergence for the deterministic finite supported
measures in rough-path H\"older metrics and determine the size of the particle
system required to accurately estimate the law of McKean Vlasov equations with
respect to the H\"older norm.

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