  The `star paradox' in phylogenetics is the tendency for a particular resolved
tree to be sometimes strongly supported even when the data is generated by an
unresolved (`star') tree. There have been contrary claims as to whether this
phenomenon persists when very long sequences are considered. This note settles
one aspect of this debate by proving mathematically that there is always a
chance that a resolved tree could be strongly supported, even as the length of
the sequences becomes very large.
