  We present a detailed analysis of large scale simulations of avalanches in
the 2D Abelian sandpile model. We compare statistical properties of two
different decompositions of avalanches into clusters of topplings and waves of
topplings. Auxiliary critical exponents are introduced and the existence of the
exponent governing the contraction of avalanches claimed in our previous work
[Priezzhev et al, PRL 76,2093 (1996)] is confirmed. We also give more
elaborated argumentation for the exact values of the exponents characterizing
the statistics of waves.
