The dynamics of growth of dendrites’ side branches is investigated experimentally during the crystallization of solutions of ammonium bromide in a quasi-two-dimensional cell. Two regimes are observed. At small values of the Peclet number a self-affine fractal forms. In this regime it is known that the mean lateral front grows as t 0.5 . Here the length of each individual branch is shown to grow (before being screened off) with a power-law behavior t α n . The value of the exponent α n ( 0.5 ⩽ α n ⩽ 1 ) is determined from the start by the strength of the initial disturbance. Coarsening then takes place, when the branches of small α n are screened off by their neighbors. The corresponding decay of the growth of a weak branch is exponential and defined by its geometrical position relative to its dominant neighbors. These results show that the branch structure results from a deterministic growth of initially random disturbances. At large values of the Peclet number, the faster of the side branches escape and become independent dendrites. The global structure then covers a finite fraction of the two-dimensional space. The crossover between the two regimes and the spacing of these independent branches are characterized.