  We calculate the theoretical evolution of the radii of all fourteen of the
known transiting extrasolar giant planets (EGPs) for a variety of assumptions
concerning atmospheric opacity, dense inner core masses, and possible internal
power sources. We incorporate the effects of stellar irradiation and customize
such effects for each EGP and star. Looking collectively at the family as a
whole, we find that there are in fact two radius anomalies to be explained. Not
only are the radii of a subset of the known transiting EGPs larger than
expected from previous theory, but many of the other objects are smaller than
the default theory would allow. We suggest that the larger EGPs can be
explained by invoking enhanced atmospheric opacities that naturally retain
internal heat. This explanation might obviate the necessity for an extra
internal power source. We explain the smaller radii by the presence in perhaps
all the known transiting EGPs of dense cores, such as have been inferred for
Saturn and Jupiter. Importantly, we derive a rough correlation between the
masses of our "best-fit" cores and the stellar metallicity that seems to
buttress the core-accretion model of their formation. Though many caveats and
uncertainties remain, the resulting comprehensive theory that incorporates
enhanced-opacity atmospheres and dense cores is in reasonable accord with all
the current structural data for the known transiting giant planets.
