Three-dimensional Navier-Stokes simulations of unstable, miscible displacements in Hele-Shaw cells are discussed. In neutrally buoyant flows, the formation of streamwise vorticity quadrupoles is shown to result in the formation of a novel inner splitting mechanism. In the presence of density differences, the interaction of these quadrupoles with a Rayleigh-Taylor instability can lead to the formation of an ‘anchor'-like structure in vertical displacements. Gravitational effects in horizontal displacements break the up/down symmetry of the flow and result in streamwise vorticity dipoles that can split the finger lengthwise.