Tadpole galaxies have a head-tail shape with a large clump of star formation at the head and a diffuse tail or streak of stars off to one side. We measured the head and tail masses, ages, surface brightnesses, and sizes for 66 tadpoles in the Hubble Ultra Deep Field (UDF) and looked at the distribution of neighbor densities and tadpole orientations with respect to neighbors. The heads have masses of 107-108 M⊙ and photometric ages of ∼0.1 Gyr for z ∼ 2. The tails have slightly larger masses than the heads and comparable or slightly older ages. The most obvious interpretation of tadpoles as young merger remnants is difficult to verify. They have no enhanced proximity to other resolved galaxies as a class, and the heads, typically <0.2 kpc in diameter, usually have no obvious double-core structure. Another possibility is ram pressure interaction between a gas-rich galaxy and a diffuse cosmological flow. Ram pressure can trigger star formation on one side of a galaxy disk, giving the tadpole shape when viewed edge-on. Ram pressure can also strip away gas from a galaxy and put it into a tail, which then forms new stars and gravitationally drags along old stars with it. Such an effect might have already been observed in the Virgo Cluster. Another possibility is that tadpoles are edge-on disks with large, off-center clumps. Analogous lop-sided star formation in UDF clump clusters is shown. © 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.