I would like to cross Poland-Ukrainian border by car owned by my friend, but friend does not go with me. I go from Poland to Ukraine and get back 10 days later. What kind of documents I should prepare for this car?
I've crossed many borders in my car and not once have I been asked to provide proof of ownership, or even been questioned about it.
However, my experience is all EU/EEA. The only crossings I have made that might have had the potential for questioning (ie. a border post with some customs/immigration presence) were: entering and leaving Switzerland from neighbouring countries; and transiting from Slovenia -> Croatia -> Hungary. Several other countries have also required a vignette of some kind, and again I was never asked about ownership of my car; just country of registration, the license plate number, and pay the fee.
That said, it is often mandatory to have the vehicle ownership documents in the car when you cross an international border, so you may have a different experience.
I'll leave it to other contributors, perhaps with experience of the Poland - Ukraine border, to say whether my experience is common or whether there are specific issues you need to consider.