Magnetized laser-produced plasmas are central to many novel laboratory astrophysics and inertial confinement fusion studies, as well as in industrial applications. Here we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume expanding in a 20 T transverse magnetic field. The plasma is collimated by the magnetic field into a slender, rapidly elongating slab, whose plasma-vacuum interface is unstable to the growth of the "classical", fluid-like magnetized Rayleigh-Taylor instability.The combination of high-power lasers with externally applied high-strength magnetic fields of up to kT [1,2] has been seminal in the development of many recent applications in laboratory astrophysics [3][4][5][6][7], in novel concepts in laser-[8-10] and magnetically-driven [11,12] inertial confinement fusion physics, and in industrial applications [13,14]. Beside understanding the dynamics of the plasma expansion across a magnetic field, of particular importance is to grasp the nature of rapidly growing instabilities which may develop and profoundly modify the morphology and characteristics of these plasmas. Indeed, the presence of striations and flutes have often been associated with the development of instabilities and in particular with the lower hybrid drift instability (LHDI) or one of its variants [15][16][17]. In addition, anomalous resitivity driven by the LHDI [18,19] can also affect the plasma microscopically, with potentially important consequences on magnetic field diffusion and the growth of other instabilities. Among those, the magnetic Rayleigh-Taylor instability (MRTI) [20,21] is known to play a key role on the dynamics of laboratory [22], as well as astrophysical plasmas [23,24]. So far however, it has not been isolated in laser-produced high energy density plasmas.A major parameter affecting the stability and dynamics of these plasmas is the relative direction of the applied magnetic field with respect to the plasma expansion axis. While for an aligned magnetic field the plasma is collimated into an axisymmetric, stable jet-like flow [4,5], for a transverse magnetic field both stable[25] and unstable flows [26] were observed and a clear understanding of the plasma evolution is still missing.Here, we provide the first complete description of the three-dimensional dynamics of a laser-driven plasma plume in a transverse 20 T magnetic field. We show that the plasma is collimated into a slender, rapidly expanding slab, and demonstrate that under these conditions, the growth of flute-like, interchange modes at the plasma-vacuum interface that extend in the form of spikes into the vacuum is due to the classical, fluid-like, magnetic Rayleigh-Taylor instability (MRTI). Interestingly, we find that to recover quantitatively in the simulations the penetration of these spikes into the vacuum, a subgrid-scale model of anomalous resistivity needs to be included. This anomalous resistivity could be induced by the micro-turbulence generated by the LHDI, which for our plasma condition...