This is a question about nonuniform circuit families that's kind of bothering me. Let $\lbrace C_n \rbrace$ be a family of circuits for a language $L$ such that for inputs $x$ of length $n$, $C_n(x) = L(x)$. This implies that $C_n$ has to answer correctly on all inputs of the form $0y$, where $|y| \leq n-1$, right? In that case, that implies that in specifying a circuit family $\lbrace C_n \rbrace$, you can leave out arbitrary long (but finite) sequences of circuits in this (infinitary) "description", and you wouldn't have lost any part of your description.
I'm sure this is not profound in the slightest, but it does seem strange to me - that for each $n$, the circuit $C_n$ subsumes all of the $C_k$ for $k < n$.