The phrase "much publicity" means a lot of attention or promotion given to something or someone, usually through media or public platforms. Full definition
We do however, want the case to get as much publicity as possible. (law.stackexchange.com)
On - court abilities aren't the only things one has to worry about, which is why the measurements have been getting so much publicity in recent years. (sbnation.com)
All publishing houses want to get as much publicity for their books as possible. (yodiwan.com)