  In this article we continue from \cite{sub2-1} the study of normal analytic
compactifications of $\cc^2$ from the point of view of their associated pencils
of jets of curve germs centered at infinity. If $\bar X$ is a normal analytic
compactification of $\cc^2$ which is {\em primitive}, i.e.\ $\bar X \setminus
\cc^2$ is irreducible curve, then we show that $\bar X$ is projective iff $\bar
X$ is algebraic iff at least one of the jets in the associated pencil of jets
of curve-germs can be represented by a planar curve with one place at infinity.
As a result we show that there are primitive normal analytic compactifications
of $\cc^2$ which are {\em not} algebraic. We give explicit criteria for
determining if the primitive compactification corresponding to a jet of curve
germs at infinity is projective or not.
