Private browsing? cookies enabled?

Greetings,

No, cookies are not disabled in private browsing; saving of cookies and history is disabled. This is covered in Safari's Help menu, under Private Browsing.

That file is being downloaded by an advertiser for whatever website you were at when it happened. If you disable JavaScript in Preferences>Security, that should stop it, but you'll also be unable to access or view a lot of content on many, many web sites. A more effective way of blocking those is to add the domain of the advertiser to your Hosts file.

You could also use the CSS file from FloppyMoose to block ads from many web sites, and/or use the blocking list provided by Hostal.

What is my Hosts file?

Your Hosts file is what the System refers to at boot time so that it ignores certain domains when you're on the Internet. If you go to the Finder and select Go>Go to Folder…, then type in /etc and press Return, it will take you to that invisible folder, where you'll find the Hosts file.

Open it with any text editor and you should see how it's setup for each domain that is ignored. You just need to add the domain for that advertiser, then save the changes and restart your Mac to test it out.

It's not an ad, it's some file 0kb which cannot be opened.

It is an ad; it was served from an advertiser to that site. You just need to determine the domain of the advertiser before you can add it to the Hosts file. That might be found using Get Info on the file or folder, or looking at the Activity window in Safari when you're on the site and looking through the files listed to find the advertiser(s).

I cannot believe someone out there can upload a file to by desktop with me being asked about it.

No file was uploaded. An empty file was downoaded, but that's due to JavaScript being enabled and the advertiser coding that into the ad. You can block the ads using the method I described, disable JavaScript, and/or complain to the webmaster or web site owners about that advertiser and demand they stop that practice.

The culprit is outbrain.com, and the domain they're serving those downloads from is odb.outbrain.com. So if you add that to your Hosts file and then restart your Mac and go to one of those sites again, no mysterious downloads will happen.

Unfortunately, you'll have to use the Pico editor to add the domain to the Hosts file or use Hostal, which has a whole long list of blocked domains and ad blocks ready to use. It costs money, but at least then you can easily enable/disable domains at your leisure using a GUI, and it will not give you problems in saving the file due to permissions issues.

Who says it's outbrain.com?

Because so far they are the only ones doing this.

You don't have to go to their site for this to happen; the downloads are being initiated from that site, which is why you want to block them in your Hosts file or turn off JavaScript.