  The effective average action (EAA) is a scale dependent effective action
where a scale $k$ is introduced via an infrared regulator. The $k-$dependence
of the EAA is governed by an exact flow equation to which one associates a
boundary condition at a scale $\mu$. We show that the $\mu-$dependence of the
EAA is controlled by an equation fully analogous to the Callan-Symanzik
equation which allows to define scaling quantities straightforwardly.
Particular attention is paid to composite operators which are introduced along
with new sources. We discuss some simple solutions to the flow equation for
composite operators and comment their implications in the case of a local
potential approximation.
