We develop a general regularized thin-fibre (string) model to predict the properties of non-Newtonian fluid fibres generated by centrifugal spinning. In this process the fibre emerges from a nozzle of a spinneret that rotates rapidly around its axis of symmetry, in the presence of centrifugal, Coriolis, inertial, viscous/shear-thinning, surface tension and gravitational forces. We analyse the effects of five important dimensionless groups, namely, the Rossby number (
$Rb$
), the Reynolds number (
$Re$
), the Weber number (
$We$
), the Froude number (
$Fr$
) and a power-law index (
$m$
), on the steady state trajectory and thinning of fibre radius. In particular, we find that the gravitational force mainly affects the fibre vertical angle at small arc lengths as well as the fibre trajectory. We show that for small
$Rb$
, which is the regime of nanofibre formation in centrifugal spinning methods, rapid thinning of the fibre radius occurs over small arc lengths, which becomes more pronounced as
$Re$
increases or
$m$
decreases. At larger arc lengths, a relatively large
$We$
results in a spiral trajectory regime, where the fibre eventually recovers a corresponding inviscid limit with a slow thinning of the fibre radius as a function of the arc length. Viscous forces do not prevent the fibre from approaching the inviscid limit, but very strong surface tension forces may do so as they could even result in a circular trajectory with an almost constant fibre radius. We divide the spiral and circular trajectories into zones of no thinning, intense thinning and slow or ceased thinning, and for each zone we provide simple expressions for the fibre radius as a function of the arc length.