Extremely metal poor galaxies are primitive objects attending to their chemical evolution. For reasons not well understood, they tend to have cometary or 'tadpole' morphology, with a bright peripheral clump ('the head') on a faint tail. Tadpole galaxies are rare in the nearby universe but turn out to be very common at high redshift, where they are usually interpreted as disk galaxies in early stages of assembling. If this interpretation is correct, local tadpole galaxies would be ideal to study in detail the formation of disks, which is a critical process in the pathway to galaxy formation. In an effort to elucidate their true nature, we have analyzed photometrically and spectroscopically a representative sample of local tadpole galaxies. They turn out to rotate, with the bright heads being giant HII regions displaced with respect to the rotation center. The oxygen metallicity estimated from [NII]6583/Halpha often shows significant spatial gradients across the galaxies (sim 0.5 dex), being smallest at the head and larger elsewhere. The resulting chemical abundance gradients are opposite to the ones observed in local spirals, but agrees with disk galaxies at high redshift. We interpret the metallicity variation as a sign of recent external gas accretion (cold-flows) onto the head of the tadpole. All these results combined are consistent with the local tadpole galaxies being primitive disks, with their star formation sustained by accretion of external metal poor gas.