Using spectroscopic data presented in Magrini et al. (2003), we have analyzed with the photoionization code CLOUDY 94.00 (Ferland et al. 1998) 11 Planetary Nebulae belonging to the spiral galaxy M 33. Central star temperatures and nebular parameters have been determined. In particular the chemical abundances of He/H, O/H, N/H, Ar/H, and S/H have been measured and compared with values obtained via the Ionization Correction Factors (ICFs) method, when available. Chemical abundance relationships have been investigated; in particular, a correlation between N/H and N/O similar to the Galactic one (Henry 1989), and a feeble anti-correlation between O/H and N/O have been found. A gradient in O/H across the disc of M~33 is indicatively consistent with the one found from HII regions in this galaxy (Vilchez et al 1988). Further studies in the more external parts of M~33 are however needed to ascertain this point. The present result shows that oxygen and helium abundances (with lower accuracy also nitrogen, argon and sulphur) can be actually estimated from the brightest PNe of a galaxy, even if the electron temperature cannot be measured. We also found that the oxygen abundance is quite independent of the absolute magnitude of the PN and consequently the brightest PNe are representative of the whole PN population. This represents an important tool to measure the metallicity of galaxies at the time of the formation of PNe progenitors.

17 pages, 6 figures, A&A accepted