The mean first passage time (MFPT) for photoexcitations diffusion in a funn
eling potential of artificial treelike light-harvesting antennas (phenylace
tylene dendrimers with generation-dependent segment lengths) is computed. E
ffects of the nonlinearity of the realistic funneling potential and slow ra
ndom solvent fluctuations considerably slow down the center-bound diffusion
beyond a temperature-dependent optimal size. Diffusion on a disordered Cay
ley tree with a linear potential is investigated analytically. At low tempe
ratures we predict a phase in which the MFPT is dominated by a few paths.