We prove that the theory of open projective planes is complete and strictly
stable, and infer from this that Marshall Hall's free projective planes $(\pi^n
: 4 \leq n \leq \omega)$ are all elementary equivalent and that their common
theory is strictly stable and decidable, being in fact the theory of open
projective planes. We further characterize the elementary substructure relation
in the class of open projective planes, and show that $(\pi^n : 4 \leq n \leq
\omega)$ is an elementary chain. We then prove that for every infinite
cardinality $\kappa$ there are $2^\kappa$ non-isomorphic open projective planes
of power $\kappa$, improving known results on the number of open projective
planes. Finally, we characterise the forking independence relation in models of
the theory and prove that $\pi^\omega$ is strongly type-homogeneous.