This article is dedicated to the characterization of turbulent transport in the scrape-off layer of the Mega Ampere Spherical Tokamak [A. Sykes , Phys. Plasmas 8, 2101 (2001)] as a function of the average density (n(L)). The aim is to answer a renewed interest in this subject since the bursty character of turbulence in the scrape-off layer was shown to be caused by large-scale events with high radial velocity reaching about 1/10th of the sound speed called avaloids [G. Antar , Phys. Rev. Lett 87, 065001 (2001)]. With increasing density, turbulence and transport increase nonlinearly at the midplane while remaining almost unchanged in the target region. Using various and complementary statistical analyses, the existence of a "critical" density, at n(L)/n(G)similar or equal to 0.35 is emphasized; n(G) is the Greenwald density. Both above and below this density, intermittency decreases and avaloids play a decreasing role in the particle radial transport. This is interpreted as caused by the interplay between avaloids and the surrounding turbulent structures which mix them more efficiently with increasing density as the level of the background turbulence increases. The scaling of the different quantities with respect to the normalized density is obtained. It reveals that not only the level of turbulence and transport increase, but also the radial velocity and length scales. This increases the coupling between the hot plasma edge and the cold scrape-off layer that may explain the disruptive instability occurring at high densities. (c) 2005 American Institute of Physics.