  In this paper we use spontaneous flux production in annular superconductors
to shed light on the Kibble-Zurek scenario. In particular, we examine the
effects of finite size and external fields, neither of which is directly
amenable to the KZ analysis. Supported by 1D and 3D simulations, the properties
of a superconducting ring are seen to be well represented by analytic Gaussian
approximations which encode the KZ scales indirectly. Experimental results for
annuli in the presence of external fields corroborate these findings.
