clydebigdog, not if their shareholding increases over 19.9% as the result of a rights issue. The rational being that all the other shareholders were also given the opportunity to increase their shareholding in the same proportion with a rights issue.
I went thorough the same thing with BMB.
Increases over 19.9% are also possible without a take over bid by the "creep" provision, which allows an entity to increase it's shareholding by 3% every 6 months over and above the 19.9% limit.
There's is a bit about the relevance of a Rights Issue on this page in the "20% acquisition limit" section.