It means that they have some blood other than Shorthorn in their pedigree. It use to stay on their papers forever, now I think it eventually fades away. So I think more people will be promoting "asterik free" cattle that are truly not. JMO.
The ASA board several years ago voted in a policy to drop the asterisk I believe when the pedigree was 123/ 124 * free! My herd at the time was 90% * free but several of my calves had the * drop off and when I looked back they only had one * ancestor and it was WAY back!!!!!
A bit cynical are we? I agree with you at least the SH put an * unlike many other breeds. Angus are still standing around telling us they are pure. Went from little short pugs in the 60's to monsters in the 80's and early 90's and they did it all on selection..... yup they selected some chi and some Holstein. Black and polled covered it all up and that was that.