  A partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where
$\mathcal{P}$ is a non-empty set of points and $\mathcal{L}$ is a collection of
subsets of $\mathcal{P}$ called lines such that any two distinct points are
contained in at most one line, and every line contains at least two points. A
partial linear space is proper when it is not a linear space or a graph. A
group of automorphisms $G$ of a proper partial linear space acts transitively
on ordered pairs of distinct collinear points and ordered pairs of distinct
non-collinear points precisely when $G$ is transitive of rank 3 on points. In
this paper, we classify the finite proper partial linear spaces that admit rank
3 affine primitive automorphism groups, except for certain families of small
groups, including subgroups of $A\Gamma L_1(q)$. Up to these exceptions, this
completes the classification of the finite proper partial linear spaces
admitting rank 3 primitive automorphism groups. We also provide a more detailed
version of the classification of the rank 3 affine primitive permutation
groups, which may be of independent interest.
