It is not well understood whether the growth of early-type cluster galaxies proceeds inside-out, outside-in, or at the same pace at all radii. In this work we measured the galaxy size, defined by the radius including 80% of the galaxy light, non-parametrically. We also determined a non-parametric estimate of galaxy light concentration, which measures the curvature of the surface brightness profile in the galaxy outskirts. We used an almost random sampling of a mass-limited sample formed by 128 morphologically early-type galaxies in clusters with $log M/M_{odot} ga 10.7$ spanning the wide range $0.17<z<1.81$. From these data we derived the size-mass and concentration-mass relations, as well as their evolution. At 80% light radius, early-type galaxies in clusters are about 2.7 times larger than at 50% radius at all redshifts, and close to de Vaucouleurs profiles in the last 10 Gyr. While between $z=2$ and $z=0$ both half-light and 80% light sizes increase by a factor of $1.7$, concentration stays constant within $2$%, that is to say the size growth of early-type galaxies in cluster environments proceeds at the same pace at both radii. Existing physical explanations proposed in the literature are inconsistent with our results, demonstrating the need for dedicated numerical simulations to identify the physical mechanism affecting the galaxy structure.
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