  The X-ray afterglows (AGs) of Gamma-Ray Bursts (GRBs) and X-Ray Flashes
(XRFs) have, after the fast decline phase of their prompt emission, a temporal
behaviour varying between two extremes. A large fraction of these AGs has a
'canonical' light curve which, after an initial shallow-decay 'plateau' phase,
'breaks smoothly' into a fast power-law decline. Very energetic GRBs,
contrariwise, appear not to have a 'break', their AG declines like a power-law
from the start of the observations. Breaks and 'missing breaks' are intimately
related to the geometry and deceleration of the jets responsible for GRBs. In
the frame of the 'cannonball' (CB) model of GRBs and XRFs, we analyze the cited
extreme behaviours (canonical and pure power-law) and intermediate cases
spanning the observed range of X-ray AG shapes. We show that the entire panoply
of X-ray light-curve shapes --measured with Swift and other satellites-- are as
anticipated, on very limpid grounds, by the CB model. We test the expected
correlations between the AG's shape and the peak- and isotropic energies of the
prompt radiation, strengthening a simple conclusion of the analysis of AG
shapes: in energetic GRBs the break is not truly 'missing', it is hidden under
the tail of the prompt emission, or it occurs too early to be recorded. We also
verify that the spectral index of the unabsorbed AGs and the temporal index of
their late power-law decline differ by half a unit, as predicted.
