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If you are able to modify the HTML page, then you can add CSS between <style> ... </style> inside the header block (<head>), in case you can't add or modify an external CSS file.

I spent quite some time doing this and I'm rather happy about the result: https://florentfo.rest/publications

Only problem is the top alignment that I could not manage. As a result, if the paper has a multi-line title or authors list, the image will be placed a bit too low.

This is my CSS:

.bibbase_note img
  float: right
  position: relative
  top: -50px
  height: auto
  width: 240px
  left: -100%
  margin: auto

.bibbase_paper
  padding-left: 240px;

I see, thanks a lot for the explanation!

Interesting, so you run some kind of central database keeping track of all publication counters of all users? And is the counter tied to the website URL hosting the bibbase component, or only to the publication itself (uniquely identified in some way)? (like, would it reset to zero if I set up bibbase on another website?) 

Thanks for the very quick fix! (by the way, I wonder how this download count works ?)