We have studied the Dalitz plot of the e(+)e(-) -> pi(0)pi(0)gamma events (N(pi)0(pi)0 gamma similar to 65 000) collected at root s similar or equal to M-phi with the KLOE detector. In the dipion invariant mass (M-pi pi) region below 700MeV, the process under study is dominated by the non- resonant process e(+)e(-) -> omega pi(0) with omega -> pi(0)gamma whereas, for higher M-pi pi values, the radiative phi decay to the f(0)(980) is the dominant mechanism. Different theoretical models are used to fit the Dalitz plot, taking also into account a possible contribution of the sigma(600). For each model, we extract the f(0)(980) mass and its coupling to pi pi, K (K) over bar and to the phi.