[rich_sasha]

The limiting factor is power/distance^2 basically, which determines the signal/noise ratio, which determines the bandwidth.

A mesh network sounds fun, though you'd have to have a fair few probes, as their orbits wouldn't be in sync. Also that far from the sun, solar panela don't cut it and you need nuclear thermal generators, which have a finite lifespan.

[credit_guy]

Also the power. Juno does not have nuclear power, only solar panels. The Sun is quite dim at Jupiter’s distance.

From wikipedia:

    Power: 14 kW at Earth,435 W at Jupiter

Overall the strangth of the signal coming from a solar powered spacecraft in the outer Solar system should go down with the 4th power of the distance.