Separation of classes with different amounts of advice?
Let $s(n) \ge n$ be some function. It can be proven that:

$\mathbf{DSIZE}(s) \subseteq \mathbf{DTIME}(s^2) / F(O(s\log s))$

Here, $\mathbf{DSIZE}(s)$ denotes the set of languages decidable by deterministic circuits of size $s$. The notation $\mathbf{K/F}$ denotes the complexity class $\mathbf{K}$ with advice function from the set $\mathbf{F}$, defined as:

$F(f) = \left\{h \colon \{0,1\}^* \to \{0,1\}^* \mid |h(x)| \le f(|x|) \text{ for all } x\right\}$.

In addition, let $d(n) \ge \log n$ be another function. Then:

$\mathbf{DDEPTH}(d) \subseteq \mathbf{DSPACE}(d) / F(2^{O(d)})$

where $\mathbf{DDEPTH}(d)$ denotes the set of languages decidable by deterministic circuits of depth $d$.



Edit: two more inclusions:

For $t(n) \ge n$ we have $\mathbf{DTIME}(t) \subseteq \mathbf{DSIZE}(t \log t)$,
and for $l(n) \ge \log n$ we have $\mathbf{NSPACE}(l) \subseteq \mathbf{DDEPTH}(l^2)$.




  For proofs, see section 2-3 of Heribert Vollmer's book.


Using these inclusions, and time/space hierarchies, one can build hierarchies for non-uniform complexity classes.



Edit 2:

You may combine the above results with the following results on hierarchies for classes with advice:


Time Hierarchies for Computations with a Bit of Advice.
Unconditional Lower Bounds Against Advice.