  We introduce a family of natural normalized Loewner chains in the unit ball,
which we call "ger\"aumig"---spacious---which allow to construct, by means of
suitable variations, other normalized Loewner chains which coincide with the
given ones from a certain time on. We apply our construction to the study of
support points, extreme points and time-$\log M$-reachable functions in the
class $S^0$ of mappings admitting parametric representation.
