Could not get relativeURLs to work with {{ .Site.BaseURL }}

I was fiddling around with this the last few days and since half an hour I have a complete site (blog section and traditional home page all-in-one) working without any issues on my local file system (without using hugo server).

I use .RelPermalinks, relURL and set uglyURLs = true, relativeURLs = true, canonifyURLs = false and in fact it is essential NOT to set baseURL to anything other than http://www.domain.tld - NO additional folders are allowed here.
But as the site is truely portable you may install it anywhere on the server I think. Will test this tomorrow.