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We comment on the assertion made by Caselle et al., J. Stat. Mech. 0603, P008(2006), that the confining (string) potential for three quarks "makes a smoothcross-over transition from the Delta-string to the Y-string configuration atinterquark distances of around 0.8 fm". We study the functional dependence ofthe three-quark confining potentials due to a Y-string, and the Delta-stringand show that they have different symmetries, which lead to different constantsof the motion (i.e. they belong to different "universality classes" in theparlance of the theory of phase transitions). This means that there is no"smooth cross-over" between the two, when their string tensions are identical,except at the vanishing hyper-radius. We also comment on a certain two-bodypotential approximation to the Y-string potential.

On the smooth cross-over transition from the Delta-string to the Y-string three-quark potential