Michel,

>...The legal aspects regards to the state of California and how they would deal with such an issue where a client is refused access to advertise into a specific publishing without any other specific justifications than the term "Competitor" and how this is interfering with the liberty of advertising.

Generally speaking, a publication can accept or refuse advertising for any reason or for no stated reason at all. Many people are surprised to find out that this includes political advertising as well (it's a different story with broadcasting, as the FCC has additional rules to regulate that industry).

It would be very difficult (at least in the US) to force a print publication to take your ad. Freedom of the press means just that -- complete freedom of the publisher to decide what goes into the publication.