In this paper we use the semi-analytical approach to analyze gravitational lensing of remote objects (quasars) by dark halos in various cosmologies in order to determine the sensitivity of the predictions for probabilities of splitting-angles of multiple images to the input assumptions regarding halo properties and cosmological model. All models are variants of the cold dark matter scenario and all fail in that they predict too many occurrences of large splitting lenses. The mass function of dark halos is assumed to be given by the Press-Schechter function. The mass density profile of dark halos is alternatively taken to be the singular isothermal sphere, the NFW (Navarro-Frenk-White) density profile, and the generalized NFW density profile which has a different slope at small radii. The cosmologies being considered include: the Einstein-de Sitter model (i.e. the standard cold dark matter model), which is a flat universe without a cosmological constant; the open model, which is a universe with negative spatial curvature but without a cosmological constant; and the Λ-model, which is a flat universe wit
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