If you drag a link or favicon on the left end of the location bar onto the desktop to create an internet shortcut then that shortcut gets the icon of the default browser.
If you want a different icon (favicon) then you have to assign that icon yourself to the desktop shortcut (right-click: Properties).
You can usually get the favicon if you append "favicon.ico" to the main domain of a website (e.g. http://www.mozilla.com/favicon.ico ) to display the favicon in a tab and save that image to a folder or see if you can find it in "Tools > Page Info > Media".

I don't wish to have a default icon,i would like to have the website icon that comes with that website.that's is what very wrong with the browser

Me, too!

My desktop is covered with Firefox logos.

If Microsoft can handle it, then so should Firefox.

Since I drag the website logo, on to the desktop, why does it 'convert' to Firefox?

If you drag a link or favicon on the left end of the location bar onto the desktop to create an internet shortcut then that shortcut gets the icon of the default browser.
If you want a different icon (favicon) then you have to assign that icon yourself to the desktop shortcut (right-click: Properties).
You can usually get the favicon if you append "favicon.ico" to the main domain of a website (e.g. http://www.mozilla.com/favicon.ico ) to display the favicon in a tab and save that image to a folder or see if you can find it in "Tools > Page Info > Media".

us037608 wrote:

I don't wish to have a default icon,i would like to have the website icon that comes with that website.that's is what very wrong with the browser.

I would amend his post by omitting the 'very' - Bill