Summary: We calculate the stable pair theory of a projective surface \(S\). For fixed curve class \(\beta\in H^2(S)\) the results are entirely topological, depending on \(\beta^2\), \(\beta.c_1(S)\), \(c_1(S)^2\), \(c_2(S)\), \(b_1(S)\) and invariants of the ring structure on \(H^*(S)\) such as the Pfaffian of \(\beta\) considered as an element of \(\Lambda^2 H^1(S)^*\). Amongst other things, this proves an extension of the Göttsche conjecture to non-ample linear systems. We also give conditions under which this calculates the full 3-fold reduced residue theory of \(K_S\). This is related to the reduced residue Gromov-Witten theory of \(S\) via the MNOP conjecture. When the surface has no holomorphic 2-forms this can be expressed as saying that certain Gromov-Witten invariants of \(S\) are topological. Our method uses the results of the first part [the authors, ibid. 1, No. 3, 384–399 (2014)] to express the reduced virtual cycle in terms of Euler classes of bundles over a natural smooth ambient space.