This is somehow related to the question Are some languages known to have taken grammatical features etc rather than just lexicon from their substrate languages?
In the area of today's Turkey, Iran and parts of central Asia, the Arabic language, Persian language and Turkish languages have for a long time coexisted. Apart from lexical (mutual) borrowings of Persian and Turkish and borrowings of both from Arabic (and to a much lesser extent, as far as i know, borrowings from Persian/Middle Persian to Arabic), there are some grammatical features which Persian and Turkish have in common.
For example Persian possessive suffixes: dar (door) -> dar-am (my door), which in the first person singular even (more or less) coincide with the turkish ones. Is this or could this be some sort of grammatical borrowing? Which way?
Other coincidences are the copulative suffixes (if this may be called thus) and - but I do know of only one instance - Persian lū in kūchulū reminiscent of Turkish kücüklü/kücüklük.