The direct accretion of pristine gas streams is predicted to be the main mode of galaxy disk growth in the early universe (cold-flows). We (think we) have discovered this physical process at work in the local Universe. The finding is one of the outcomes of our in-depth study of local extremely metal poor (XMP) galaxies. I will explain the main observational properties of XMPs, in particular, their tendency 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. We have found the heads to be giant HII regions displaced with respect to the rotation center, with the galaxy metallicity being smallest at the head and larger elsewhere. The resulting chemical abundance gradient is opposite to the one observed in local spirals, and suggests a recent gas accretion episode onto the head. Thus, local XMP galaxies seem to be primitive disks, with their star formation sustained by accretion of external metal poor gas. I will argue how the same mechanism may be driving the star formation in many other local galaxies. Ongoing observational projects to confirm these findings and conjectures will be briefly mentioned.