I can only talk about the ways my parents did it for me, but I think they did a pretty good job.
Are you planning on buying them their first car?
I was provided a car--an old minivan when my parents upgraded--to drive myself to my high school extracurriculars. It was not "my" car and it passed to my next sibling when I left for college.
A few of my now-adult siblings did get to take comparable old cars with them when they flew the nest, but I bought my own first car. ($3k. Still driving it.)
Paying for their community college? Paying for their bachelor's degree at a state university? Paying for their master's degree?
The deal my parents gave us was that they'd match every dollar we put toward college. Very generously, that included merit scholarships. (In retrospect, they and I agree that I probably could and should have chosen a cheaper college than I did.) I was required to have a job on campus (I got a talking-to when it took me until November freshman year to get one) and over summers.
I was a little behind on my half of the 50-50 arrangement by the time I graduated, about $5000 in debt to them. They told me to get an emergency fund together before paying them back and didn't charge me interest, but I did pay them back within 2.5 years.
Grad school is not included in this deal.
Paying for their first house?
Definitely not! Any of their kids can live at home for free for as long as they are in school of any kind. Once you graduate, you owe rent, although it's probably well below market rate. I never did this, but my brother did. They may have gifted him the collected rent back once he moved out, though I'm not certain about that.
Are there any studies indicating if children whose parents paid 100% for their tuition do better in life vs children whose parents did not pay for their college education?
I have no idea what the studies show. My parents believed it was important for us to have some financial skin in the game to ensure we took college seriously.
How much financial support did your parents provide for you after you became an adult?
Aside from what's detailed above, they gave us a four-figure wedding gift. We may soon get an old family car for cheap or free (though frankly it's not "support," it's closer to "Nobody else wants this, do you?") They cover our share of the annual family vacation to rural family property. They're pretty generous with Christmas gifts. When we (rarely) go out for family meals, they usually pay.
When I first went to grad school, I was about to live on my own, paying rent etc., for the first time, in a VHCOL city, on $30k per year. I had no idea how much money was worth. My mom helped me put together a monthly budget and a grocery plan that would fit within that. We ran out of money in the budget on the first try, and I got super nervous about being able to afford it. She looked me in the eye like "Hmm, that's not going to work. Better start over," and helped me rework it until it fit. In other words, I got a great foundation of knowledge, but it was always very clear I was expected to sustain myself.
(This was before I found FIRE. Within a few years I had proven that I could live on half that income in that city.)
Most valuable to me today is that they've taken care of their own finances well enough that I'm not worried about having to take care of them, money wise, in their old age.