  ABRIDGED: NGC5253 is an ideal laboratory for detailed studies of starburst
galaxies. We present for the first time in a starburst galaxy a 2D study of the
spatial behavior of collisional and radiative transfer effects in He^+. The HeI
lines are analysed based on data obtained with FLAMES and GMOS. Collisional
effects are negligible for transitions in the singlet cascade while relatively
important for those in the triplet cascade. In particular, they can contribute
up to 20% of the flux in the HeIl7065 line. Radiative transfer effects are
important over an extended and circular area of 30pc in diameter centered at
the Super Star Clusters. HeI abundance, y^+, has been mapped using extinction
corrected fluxes of six HeI lines, realistic assumptions for T_e, n_e, and the
stellar absorption equivalent width as well as the most recent emissivities. We
found a mean of 10^3 y^+ ~80.3 over the mapped area. The relation between the
excitation and the total helium abundance, y_tot, is consistent with no
abundance gradient. Uncertainties in the derivation of He abundances are
dominated by the adopted assumptions. We illustrated the difficulty of
detecting a putative He enrichment due to the presence of Wolf-Rayet stars in
the main GHIIR. Data are marginally consistent with an excess in the N/He ratio
in the N enriched area of the order of both, the atmospheric N/He ratios in WR
stars and the uncertainties estimated for the N/He ratios.
