I'm not coming in as a hater here, so please don't get the wrong idea while reading my post.
I find it sort of odd folks speak of the tulpa being fully independent, and I wanted to give some of my ideas on why.
A tulpa exist within your mind. Stating the obvious here to start out slow. Everything that goes into the tulpa must come from somewhere in your mind. Yes. Even if you fully believe it is 100% independent its existence and many other factors that rely solely on you. Now if you have a spontaneous and random side to your personality you can assign this "friend" to an area of thoughts and subconscious you normally wouldn't operate in.
Even if it relies solely on your subconscious it is still not 100% independent. Now it is hard to say with schizophrenia where the being is no longer beneficial and you don't want it but it continues to reside in your mind because that is a disorder.
Now before people jump on me for hating I would like to say a few more things before ending this post.
I make a habit of going on long walks and on foot trips (longest being around 20+ miles taking roughly a 8 hours to my recollection)
and I carry on conversations and stuff while alone. Sometimes there isn't any conversation and it is me just running numerous scenarios and calculations out loud as it seems to help me think clearer and have a better train of thought.
Conversation wise it is one side of my personality essentially criticizing or going into other unimportant areas during the walk.
Essentially being along the lines of, "You said you were going to turn around a mile ago. Dude look at the time. XD".
While I'm not parroting this other side of the conversation, I fully acknowledge that it isn't some %100 independent being as I know it all originates from somewhere in my mind.
Anyways for those who think otherwise I would gladly read and look over your post regarding it.