I asked my hoster to add three subdomains all pointing to the IP of the A record. It seems he simply added a wildcard DNS record because any random subdomain resolves to my IP now. This is OK for me from a technical point of view, since there are no subdomains pointing anywhere else. Then again I don't like him not doing what I asked for. And so I wonder whether there are other reasons to tell him to change that. Are there any?
The only negative I found is that someone could link to my site using