ns4006554.ip-198-27-80.net has been visiting all sites of mine, including very recently established ones, so its visits appear to be not accidental but deliberate. Only the mainpages is accessed in each case.
This is a host, not a dynamic address, there is never a referer and only a generic browser description in the UA. This host appears to be located in Quebec, Canada (their homepage only shows the generic "Apache installed" information.
If anybody has more information I'd be interested in it. TIA :-)