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I have an unusual situation. My deployment environment needs to place pdftex and associated files into a custom directory that is not known until deploy time, and changes from one server to the next in a relatively random way. I.e. I cannot preinstall TEX on the server, and I cannot install anything into standard directories such as /etc, /usr/local, or the user's home directory. Everything needs to go into a custom directory like /path/to/deploy/here/somerandomstring.

Is there a way to make pdftex run such that it will look for files such as latex.fmt only in directories that I tell it to look in at runtime using some combination of command line arguments and environment variables?

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I have never tried it myself, but there's an option in TeX Live that allows an installation on a USB stick. This should also solve your issue. – Uwe Ziegenhagen Jan 16 '14 at 20:13
You can also override TeX's variables on the command line e.g. TEXMFHOME=/path/to/nonexistent/directory pdflatex filename.tex will ignore anything in my real TEXMFHOME. (And setting it to an existent directory would use the contents of that directory.) So you could presumably do the same for variables specifying the other texmf trees. – cfr Jan 16 '14 at 23:08

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