  Consider a geometrically finite Kleinian group $G$ without parabolic or
elliptic elements, with its Kleinian manifold $M=(\H^3\cup \Omega_G)/G$.
Suppose that for each boundary component of $M$, either a maximal and connected
measured lamination in the Masur domain or a marked conformal structure is
given. In this setting, we shall prove that there is an algebraic limit
$\Gamma$ of quasi-conformal deformations of $G$ such that there is a
homeomorphism $h$ from $\mathrm{Int} M$ to $\H^3/\Gamma$ compatible with the
natural isomorphism from $G$ to $\Gamma$, the given laminations are
unrealisable in $\H^3/\Gamma$, and the given conformal structures are pushed
forward by $h$ to those of $\H^3/\Gamma$. Based on this theorem and its proof,
in the subsequent paper, the Bers-Thurston conjecture, saying that every
finitely generated Kleinian group is an algebraic limit of quasi-conformal
deformations of minimally parabolic geometrically finite group, is proved using
recent solutions of Marden's conjecture by Agol, Calegari-Gabai, and the ending
lamination conjecture by Minsky collaborating with Brock, Canary and Masur.
