  The aim of this work is to derive sharp quantitative estimates of the
qualitative convergence results developed in [28] for regularized full- and
partial-cloaks via the transformation-optics approach. Let $\Gamma_0$ be a
compact set in $\mathbb{R}^3$ and $\Gamma_\delta$ be a $\delta$-neighborhood of
$\Gamma_0$ for $\delta\in\mathbb{R}_+$. $\Gamma_\delta$ represents the virtual
domain used for the blow-up construction. By incorporating suitably designed
lossy layers, it is shown that if the generating set $\Gamma_0$ is a generic
curve, then one would have an approximate full-cloak within $\delta^2$ to the
perfect full-cloak; whereas if $\Gamma_0$ is the closure of an open subset on a
flat surface, then one would have an approximate partial-cloak within $\delta$
to its perfect counterpart. The estimates derived are independent of the
contents being cloaked; that is, the cloaking devices are capable of nearly
cloaking an arbitrary content. Furthermore, as a significant byproduct, our
argument allows the relaxation of the convexity requirement on $\Gamma_0$ in
[28], which is critical for the Mosco convergence argument therein.
