In 1981 Parisi and Sourlas conjectured exact critical exponents for 
Self-Avoiding Branched Polymers in D = 2,3 dimensions.  We prove these 
conjectures.  We also obtain the exponents in D = 4 dimensions by analytically continuing Baxter's solution to the Hard Hexagon model to negative activities.  We relate these values to those obtained from Flory theory and from the epsilon expansion.