  Given a set of simplifying moves on 3-manifolds, we apply them to a given
3-manifold M as long as possible. What we get is a root of M. For us, it makes
sense to consider three types of moves: compressions along 2-spheres, proper
discs and proper annuli having boundary circles in different components of the
boundary of M. Our main result is that for the above moves the root of any
3-manifold exists and is unique. The same result remains true if instead of
manifolds we apply the moves to 3-cobordisms.
