Pinch-off dynamics of liquid threads of power law fluids surrounded by a passive ambient fluid are studied theoretically by fully two-dimensional (2-D) computations and one-dimensional (1-D) ones based on the slender-jet approximation for 0 < n <= 1, where n is the power law exponent, and 0 <= Oh <= infinity, where Oh mu(0)/root rho sigma R is the Ohnesorge number and mu 0, rho, sigma, and R stand for the zero-deformation-rate viscosity, the density, the surface tension, and the initial thread radius, to develop a comprehensive understanding of breakup which has heretofore been lacking. Under the assumption that the thread shape at breakup is slender, Doshi et al. [J. Non-Newtonian Fluid Mech. 113 (2003) 1] showed that inertial, viscous, and capillary forces must remain in balance as the minimum thread radius h(min) -> 0 and that in this inertial-viscous power law (IVP) regime, where Oh = 1, the radial length h, the axial length z, and the axial velocity v must scale with time to breakup tau as h similar to tau(n), z similar to t(1-n/2), and v similar to t(-n/2). Doshi et al. further deduced that in the viscous power law (VP) regime, in which a pinching thread undergoes creeping flow and Oh = infinity, h similar to tau(n), z similar to tau(delta), where 0.175 <= delta is the axial scaling exponent that rises as n falls, and v similar to tau(delta-1). Doshi et al. recognized that the slenderness assumption is violated when n falls below a certain value. The critical value of n is 2/3 in the IVP regime and, as shown by Renardy and Renardy [J. Non-Newtonian Fluid Mech. 122 (2004) 303], 0.54 in the VP regime. When viscous force is indentically zero (Oh = 0), it has been known for some time that in this potential flow (PF) regime thread shapes at breakup are non-slender and overturned, and that h similar to t(2/3), z similar to tau(2/3), and v similar to tau(-1/3). Here, the 2-D computations are used to show that the scaling exponents of radial and axial lengths are equal and that h similar to tau(n), z similar to tau(n), and v similar to tau(n-1) when n <= 0.54 in creeping flow, which is henceforward referred to as the non-slender viscous power law (NSVP) regime. For Newtonian fluids (n = 1), the creeping flow and the potential flow regimes are transitory, and a pinching thread of a high (low) viscosity fluid must ultimately transition to a final asymptotic regime in which inertial, viscous, and capillary forces all diverge but remain in balance as pinch-off nears. Here, the 2-D computations are used to demonstrate that pinching threads of power law fluids exhibit remarkably richer response compared to their Newtonian counterparts. When Oh = I and n < 2/3, the 2-D computations show that a thread of a power law fluid asymptotically thins according to the potential flow (PF) scaling law as if it were an inviscid fluid and that its profile is non-slender and overturned in the vicinity of the pinch-point. When Oh > 1, the 2-D computations reveal that a thinning thread transitions from the VP to the IVP regime when n > 2/3 in accordance with the I-D results but a thinning thread transitions from the VP to the PF regime when 0.54 < n <= 2/3 and from the NSVP regime to the PF regime when n < 0.54. When Oh < 1, the 2-D computations show that a thinning thread transitions from the PF to the IVP regime when n > 2/3 in accordance with the I-D results but a thinning thread remains in the PF regime until reakup when n << 2/3. Moreover, when Oh << 1 and n > 2/3, the 2-D computations show that the interface overturns first before the thread transitions from the PF to the IVP regime. When Oh < I and n > 2/3, the transition between the PF and the IVP regimes is shown to occur when the minimum thread radius h(min) similar to Oh(2/(3n-2)). Scaling exponents and self-similar thread shapes and axial velocity profiles obtained from the 2-D computations are shown to be in excellent agreement with the I-D results when thread shapes at breakup are slender. (c) 2006 Elsevier B.V. All rights reserved.