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We continue the investigation of the distribution of $\ell^{\infty}$-Selmergroups in degree $\ell$ twist families of Galois modules over number fieldsbegun in the previous paper. Building off the work on higher Selmer groups inthat part, we find conditions under which we can compute the distribution ofthe $\ell^{\infty}$-Selmer groups for a given degree $\ell$ twist family. Alongthe way, we show that the average rank in the quadratic twist family of anygiven abelian variety over a number field is bounded.

The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II