I wish he did publish the Daily Mail, as it would give me more mockery ammo to use against my girlf, who works for the Mail's toehold in Ireland, but he doesn't. Associate Newspapers does.
Desmond is owner of the Daily Express, not the Daily Mail.
However some non-UK (?) confusion is understandable. Until Desmond switched to 'supporting' the Labour government in 2001, the Mail and the Express were pretty indistinguishable in terms of content.
In his own words, Richard Desmond is a purveyor of "barely legal teens for the connoisseurs of young beauty". Go figure. Yes, the Daily Mail is ghastly.