Going through the hassle of getting a title for stuff you'll scrap is, ugh, an ill advised use of time unless your goal is to tell everyone at the cocktail party how law abiding you are or the vehicles are interesting enough for the title to have baseline value or something like that.
Scrapyards will take fractions of cars without asking questions. People who part out cars or deal in scrap metal know this and will take anything off your hands for free as long as the work vs what they're getting pencils out.
Scrapyards are also places the police investigate as money laundering for crime. They will take untitled things, but only if they think it wasn't stolen. Start bringing in too much scrap vehicle parts and they will start demanding paperwork - one or two parts "everyone" has so no not worth it but if it gets to be a bunch they start suspecting crime and then demand paperwork.
Just saw it up so it's not obviously one complete car. Nobody cares as long as their ass is covered. You can get away with more if you're a regular and they know you and know you not to be sketchy.
Even if they know you they'll never take a full car body in one piece without a title or any of the other "open and shut case" violations of law because they don't wanna risk getting Randy Weaver'd because a good customer had government problems and became an "informant".
Scrapyards will take fractions of cars without asking questions. People who part out cars or deal in scrap metal know this and will take anything off your hands for free as long as the work vs what they're getting pencils out.