Have there ever been any studies or surveys of reasonably significant size that indicate how many Catholics believe in transubstantiation or would at least claim that they do?
Pew research does some awesome polls on questions like this.
About half of those polled (52%) say, incorrectly, that Catholicism teaches that the bread and wine used for Communion are symbols of the body and blood of Jesus. Just four-in-ten people correctly answer that, according to the Catholic Church, the bread and wine actually become the body and blood of Jesus. Even many Catholics are unaware of their church’s teaching on this topic; while 55% of Catholics get the question right, more than four-in-ten Catholics (41%) say the church teaches that the bread and wine are symbols of Christ’s body and blood, and 3% say they do not know what the church’s teaching is. Still, Catholics perform better on this question than does any other religious group.
Also this site made a nice graphic.
In conclusion I think it's safe to say that about 40-50% of Catholics believe in the real presence. I hope that helps!