[tex-live] include directories to search for additonal fileslike *.bib *.sty, etc.

[Karl Berry]

    set BIBINPUTS=.;bib
    set TEXINPUTS=.;tex\sty

    then bibtex find my bib data but latex doesn't find the class book.cls ???
    Strange. Isn't it?

No.  Expected.  Read the "default expansion" section of kpathsea.
When you define TEXINPUTS as .;tex\sty, you're telling TeX to look in
*only* those two directories.  A trailing semicolon, as in:
    set TEXINPUTS=.;tex\sty;
will tell TeX to look also in the "system" directories, which is what
you want.

    btw: The setup-process of TeX-Live (tlmgr) doesn't set any var in the
    systems or user environment. 

Completely intended.  The current state of things is for normal
operation to require *no* environment variable settings.  Such settings
have been the cause of much agony on everyone's parts over the years.

You have to set envvars only because you want to use special directories
that are (a) not the current directory and (b) not under TEXMFHOME.

    I'm new to texlive and for me it looks like that the BIBINPUTS and
    the TEXNPUTS overwrite some "defaults"

Not exactly.  See above.

Happy searching,
Karl