  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.
