We examine p-branes in AdS D in two limits where they exhibit partonic behavior: rotating branes with energy concentrated to cusp-like solitons; tensionless branes with energy distributed over singletonic partons on the Dirac hypercone. Evidence for a smooth transition from cusps to partons is found. First, each cusp yields D − 2 normal-coordinate bound states with protected frequencies (for p > 2 there are additional bound states); and can moreover be related to a short open p-brane whose tension diverges at the AdS boundary leading to a decoupled singular CFT at the "brane at the end-of-the-universe". Second, discretizing the closed p-brane and keeping the number N of discrete partons finite yields an sp(2N )-gauged phase-space sigma model giving rise to symmetrized Ntupletons of the minimal higher-spin algebra ho 0 (D − 1, 2) ⊃ so(D − 1, 2). The continuum limit leads to a 2d chiral sp(2)-gauged sigma model which is critical in D = 7; equivalentá la Bars-Vasiliev to an su(2)-gauged spinor string; and furthermore dual to a WZW model in turn containing a topological so(6, 2) −2 /( so(6) ⊕ so(2)) −2 coset model with a chiral ring generated by singleton-valued weight-0 spin fields. Moreover, the two-parton truncation can be linked via a reformulationá la Cattaneo-Felder-Kontsevich to a topological open string on the phase space of the D-dimensional Dirac hypercone. We present evidence that a suitable deformation of the open string leads to the Vasiliev equations based on vector oscillators and weak sp(2)-projection. Geometrically, the bi-locality reflects broken boundary-singleton worldlines, while Vasiliev's intertwiner κ can be seen to relate T and R-ordered deformations of the boundary and the bulk of the worldsheet, respectively.