Let K be an imaginary quadratic number field with p-Sylow-class group A(K) and L/K be an unramified cyclic extension of K of degree p (p prime). Then I am looking for heuristics on 
 
                Ker(N_{L/K}:A(L)\rightarrow A(K)), where

$N_{L/K}$ is the usual norm map on ideal classes. Numerical data suggest that:

 $|KerN_{L/K}|\le p^2$ with high probability. But that is rather unprecise. Are there any more satisfactory known results ?

There is a result by Wittmann who gives some heuristics for cyclic p-extensions of $\mathbb{Q}$ and I wonder if one can possibly generalize his ideas to the above scenario.