  We study the difference between the standard seeded model of tile
self-assembly, and the "seedless" two-handed model of tile self-assembly. Most
of our results suggest that the two-handed model is more powerful. In
particular, we show how to simulate any seeded system with a two-handed system
that is essentially just a constant factor larger. We exhibit finite shapes
with a busy-beaver separation in the number of distinct tiles required by
seeded versus two-handed, and exhibit an infinite shape that can be constructed
two-handed but not seeded. Finally, we show that verifying whether a given
system uniquely assembles a desired supertile is co-NP-complete in the
two-handed model, while it was known to be polynomially solvable in the seeded
model.
