I thought that ある was used for ownership and 持つ/持っている meant that you were carrying or holding something.
I have a computer
I'm holding a computer
Trouble is that the latter is also frequently translated as "I have a computer". I asked a native, and they said that they'll often use 持っている for ownership even if they're not/can't hold it (e.g. "車を持っているじゃん？"). The English course on Japanese Duolingo does this, and I've seen manga translate it this way as well. Is this idiomatic language that English doesn't have one word to encapsulate?