  Let $F$ be a number field and $p$ an odd prime. We estimate the kernels and
cokernels of the codescent maps of the \'etale wild kernels over various
$p$-adic Lie extensions. For this, we propose a novel approach of viewing the
\'etale wild kernel as an appropriate fine Selmer group in the sense of
Coates-Sujatha. This viewpoint reduces the problem to a control theorem of the
said fine Selmer groups, which in turn allows us to employ the strategies
developed by Mazur and Greenberg. As applications of our estimates on the
kernels and cokernels of the codescent maps, we establish asymptotic growth
formulas for the \'etale wild kernels in the various said $p$-adic Lie
extensions. We then relate these growth formulas to the Greenberg's conjecture
(and its noncommutative analogue). Finally, we shall give some examples to
illustrate our results.
