  We study the growth of the clustering dipole of galaxies from the Two Micron
All Sky Survey (2MASS). We find that the dipole does not converge before the
completeness limit of the 2MASS Extended Source Catalog, i.e. up to about 300
Mpc/h. We compare the observed growth of the dipole with the theoretically
expected, conditional growth for the LambdaCDM power spectrum and cosmological
parameters constrained by WMAP. The observed growth turns out to be within
1-sigma confidence level of the theoretical one, once the proper observational
window of the 2MASS flux dipole is included. For a contrast, if the adopted
window is a top hat, then the predicted dipole grows significantly faster and
converges to its final value at a distance of about 200 Mpc/h. We study the
difference between the top-hat window and the window for the flux-limited 2MASS
survey and we conclude that the growth of the 2MASS dipole at effective
distances greater than 200 Mpc/h is only apparent. Eventually, since for the
window function of 2MASS the predicted growth is consistent with the observed
one, we can compare the two to evaluate beta = (Omega_m)^0.55 / b. The result
is beta = 0.38+-0.05, which gives a rough estimate of Omega_m = 0.2+-0.1.
