Now i have this:

<Directory ~ "^/home/.*">
php_flag open_basedir "/home/$1"

But that does not work. How do i make reference to that .*?

Difficult. Apache doesn't interpret any variable configurations in directives. You should use %1 style RewriteCond backreferences in certain, or %{DOCUMENT_ROOT} even. But many directives use static values.

Particularly PHPs Apache SAPI doesn't make an effort to interpret any % or $ sequences.

You will find a couple of workarounds for auction on Serverfault: Using variables in Apache config files to reduce duplication?. But neither mod_macro or mod_define will accomplish what you would like. You'll have to define it for every home directory individually. (That's also what Plesk and Confixx do for multiple accounts.)