Danbooru-based image board with a specialization in high-quality images.
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Does here a
'wider than large' tag for the pics exist?
No. Assuming you're talking about the image dimensions (width, height), they are not tagged here except for wallpaper resolutions with the wallpaper tag.
But not every picture, which could be good for my background, is a wallpaper!!
You're free to search dimension sizes in the search field...

http://moe.imouto.org/help/cheatsheet said:
width:100
Search for posts with a width of 100 pixels (uses same syntax as id search).
height:100
Search for posts with a height of 100 pixels (uses same syntax as id search)
There's some more useful search hints on the cheatsheet.

Alternatively if you're looking for wallpapers, go to konachan.com ?
Revil said:
But not every picture, which could be good for my background, is a wallpaper!!
If you use DisplayFusion you can make a image fit your screen(width wise)... I think
Revil said:
But not every picture, which could be good for my background, is a wallpaper!!
Konachan does wallpapers only.
Would be easier with:
width>height
Well,
height:>width and width:>height exist but for what?
Revil said:
Would be easier with:
width>height
order:landscape, or try order:portrait.

More at cheat sheet extended.
Didn't see this version.
Thanks.