  We study the $\Lambda$-module structure of the ordinary parts of the
arithmetic cohomology groups of modular Jacobians made out of various towers of
modular curves. We prove that the ordinary parts of $\Lambda$-adic Selmer
groups coming from two different towers have "almost same" $\Lambda$-module
structures. We also prove the cotorsionness of $\Lambda$-adic Tate-Shafarevich
group under mild assumptions.
