  Skylines emerged as a useful notion in database queries for selecting
representative groups in multivariate data samples for further decision making,
multi-objective optimization or data processing, and the $k$-dominant skylines
were naturally introduced to resolve the abundance of skylines when the
dimensionality grows or when the coordinates are negatively correlated. We
prove in this paper that the expected number of $k$-dominant skylines is
asymptotically zero for large samples when $1\le k\le d-1$ under two reasonable
(continuous) probability assumptions of the input points, $d$ being the
(finite) dimensionality, in contrast to the asymptotic unboundedness when
$k=d$. In addition to such an asymptotic zero-infinity property, we also
establish a sharp threshold phenomenon for the expected ($d-1$)-dominant
skylines when the dimensionality is allowed to grow with $n$. Several related
issues such as the dominant cycle structures and numerical aspects, are also
briefly studied.
