  Given two maps f1 and f2 from the sphere Sm to an n-manifold N, when are they
loose, i.e. when can they be deformed away from one another? We study the
geometry of their (generic) coincidence locus and its Nielsen decomposition. On
the one hand the resulting bordism class of coincidence data and the
corresponding Nielsen numbers are strong looseness obstructions. On the other
hand the values which these invariants may possibly assume turn out to satisfy
severe restrictions, e.g. the Nielsen numbers can only take the values 0, 1 or
the cardinality of the fundamental group of N. In order to show this we compare
different Nielsen classes in the root case (where f1 or f2 is constant) and we
use the fact that all but possibly one Nielsen class are inessential in the
selfcoincidence case (where f1 = f2). Also we deduce strong vanishing results.
