  We show that the mode-locking region of the family of quasi-periodically
forced Arnold circle maps with a topologically generic forcing function is
dense. This gives a rigorous verification of certain numerical observations in
\cite{DGO} for such forcing functions. More generally, under some general
conditions on the base map, we show the density of the mode-locking property
among dynamically forced maps (defined in \cite{Zha}) equipped with a topology
that is much stronger than the $C^0$ topology, compatible with smooth fiber
maps. For quasi-periodic base maps, our result generalizes the main results in
\cite{ABD, WZJ, Zha}.
