  In a recent paper~\cite{DDL10} we studied basic properties of partial
immersions and partially free maps, a generalization of free maps introduced
first by Gromov in~\cite{Gro70}. In this short note we show how to build
partially free maps out of partial immersions and use this fact to prove that
the partially free maps in critical dimension introduced in Theorems 1.1-1.3
of~\cite{DDL10} for three important types of distributions can actually be
built out of partial immersions. Finally, we show that the canonical contact
structure on $\bR^{2n+1}$ admits partial immersions in critical dimension for
every $n$.
