  We study the growth of the Tate-Shafarevich and p-infinity Selmer groups for
isogenous abelian varieties in towers of number fields, with an emphasis on
elliptic curves. The growth types are usually exponential, as in the setting of
`positive mu-invariant' in Iwasawa theory of elliptic curves. The towers we
consider are p-adic and l-adic Lie extensions for l<>p, in particular
cyclotomic and other Z_l-extensions.
