Apparently, the SDSS-UKIDSS offset in the Petrosian magnitudes comes from
the difference in Petrosian radii. The radii depend on the surface
brightness which can be estimated as modelmag_r+5*log10(petror50_r).
Apparently, the values are corrected for the cosmological dimming, so the
best ``independent'' variable turns to be
S_P=modelmag_r+5*log10(petror50_r)-10*log10(1+z).

The polynomial-based correction (Y_Z_Offset_total) does not work for objects
exhibiting strong H-alpha contribution to the i band at 0.03<z<0.28 and
affecting both, r-i, and i-z colours. There are two distinct regions visible
in the derived "Y_Z_Offset_total" vs S_P parameter space (tried many options
for the third parameter without success). Strange enough, but there is no
such strong distinction on the "yPetroMag+5*log10(yGausig)-10*log10(1+z)"
diagram. Maybe, a combination of this parameter and S_P will do the better
job, still has to be checked.

The lower brench on the "Y_Z_Offset_total" vs S_P diagram corresponds to the
galaxies without significant H-alpha emission (if any). It is will
approximated by the following empirically chosen function:
(-0.07*(modelmag_r+5*log10(petror50_r)-10*log10(1+z_1)-14.0)-0.007*pow(modelmag_r+5*log10(petror50_r)-10*log10(1+z_1)-14.5,2)-0.0014*pow(modelmag_r+5*log10(petror50_r)-10*log10(1+z_1)-15.0,4))

or in the IDL syntax:

s_p = res.modelmag_r + 5*alog10(res.petror50_r) - 10*alog10(1.0+res.z)
Z_Y_OFFSET_model=(s_p lt 13.97)? 0 : -0.07*(s_p-14.0)-0.007*(s_p-14.5)^2-0.0014*(s_p-15.0)^4 


It seems there is also a *constant* offset of about 0.5 mag between SDSS and GALEX NUV.
Still to be checked.