<p>We present a systematic study of baryonic flux tubes in SU(3) Yang-Mills theory in (2+1) dimensions. A recent next-to-leading-order derivation within the Effective String Theory framework has, for the first time, made explicit the corrections proportional to the mass of the baryon junction <i>M</i>, up to order 1/<i>R</i>² (where <i>R</i> is the length of the confining strings), opening the possibility of its non-perturbative determination. One of the main goals of this paper is, through high precision simulations of the three-point Polyakov loop correlator, to measure for the first time the baryon junction mass. By isolating the predicted 1/<i>R</i>² term in the open string channel, we obtain the value <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(M/\sqrt{\sigma }=0.1355\left(36\right)\)</EquationSource> </InlineEquation>, similar to the phenomenological value which is used to describe hadrons, although our computation was done in (2 + 1) dimensions. In addition, studying the high temperature behavior of the baryon, we present a new test of the Svetitsky-Yaffe conjecture for the SU(3) theory in three dimensions. Focusing on the high temperature regime, just below the deconfinement transition, we compare our lattice results for Polyakov loop correlators with the quantitative predictions obtained by applying conformal perturbation theory to the three-state Potts model in two dimensions and find excellent agreement.</p>