The central parsec of our Galaxy hosts a population of young stars. At distances of r similar to 0.03-0.5 pc, most of these stars seem to form a system of mutually inclined discs of clockwise and counterclockwise rotating stars. We present a possible warped disc origin scenario for these stars assuming that an initially flat accretion disc becomes warped due to a central radiation source via the Pringle instability or due to a spinning black hole via the Bardeen-Petterson effect before it cools, fragments and forms stars. From simple arguments, we show that this is plausible if the star formation efficiency is high, epsilon(SF) less than or similar to 1, and the viscosity parameter alpha similar to 0.1. After fragmentation, we model the disc as a collection of concentric, circular rings tilted with respect to each other, and construct time evolution models of warped discs for mass ratios and other parameters relevant to the Galactic Centre environment, but also for more massive discs. We take into account the disc's self-gravity in the non-linear regime and the torques exerted by a slightly flattened surrounding star cluster. Our simulations show that a self-gravitating low-mass disc (M-d/M-bh similar to 0.001) precesses with its integrity maintained in the lifetime of the stars, but precesses essentially freely when the torques from a non-spherical cluster are included. An intermediate-mass disc (M-d/M-bh similar to 0.01) breaks into pieces, which precess as independent discs in the self-gravity-only case, and become disrupted in the presence of the star cluster torques. Finally, for a high-mass disc (M-d/M-bh similar to 0.1), the evolution is dominated by self-gravity and the disc is broken but not dissolved. The time-scale after which the disc breaks into pieces scales almost linearly with M-d/M-bh for self-gravitating models. Typical values are longer than the age of the stars for M-d/M-bh similar to 0.001, and are in the range similar to 8 x 10(4)-10(5) yr for M-d/M-bh similar to 0.1-0.01, respectively. None of these discs explains the two Galactic Centre discs with their rotation properties. A comparison of the models with the better defined clockwise rotating disc shows that the lowest mass model in a spherical star cluster matches the data best.