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We explore the stringy structure of 1/2-BPS bound states of NS fivebranes carrying momentum or fundamental string charge, in the decoupling limits leading to little string theory and to AdS3/CFT2 duality. We develop an exact worldsheet description of these states using null-gauged sigma models, and illustrate the construction by deriving the closed-form solution sourced by an elliptical NS5-F1 supertube. The Calabi-Yau/Landau-Ginsburg correspondence maps this geometrical worldsheet description to a non-compact LG model whose superpotential is determined by the fivebrane source configuration. Singular limits of the 1/2-BPS configuration space result when the fivebrane worldvolume self-intersects, as can be seen from both sides of the CY/LG duality - on the Landau-Ginsburg side from the degeneration of the superpotential(s), and on the geometrical side from an analysis of D-brane probes. These singular limits are a portal to black hole formation via the condensation of the branes that are becoming massless, and thus exhibit in the gravitational bulk description the central actors in the non-gravitational dual theory underlying black hole thermodynamics.