Does scalar field collapse produce `zero mass' black holes?
  An exact one parameter ($\alpha$) family of solutions representing scalar field collapse is presented. These solutions exhibit a type of critical behaviour which has been discussed by Choptuik. The three possible evolutions are outlined. For supercritical evolution (when black holes form) I show that a quantity related to the mass of the black hole exhibits a power law dependence on $\alpha$, for near critical evolution $M \simeq |\alpha-\alpha_{\rm crit}|^{1/2}$. Based on the properties of the solution some comments are also made on conjectures of Choptuik. 
Patrick R. Brady