“It depends” doesn’t answer the question of “what distance”, but max distance depends on engineering more than limitations imposed by physics.
1) What is the signal/noise ratio you require? The background noise will depend on the frequency you chose and the direction the spacecraft is communicating from.
2) What is the effective area, aperture efficiency and gain of the receiving antennae?
An example given in https://en.wikipedia.org/wiki/Parabolic_antenna is a 25m satellite ground antenna at 21cm which gives a gain of 52 dBi. The Deep Space Network 70 meter dishes have gain of 74dBi
For 2.5cm-12m waves, the atmosphere is transparent so the antennae can be ground-based. Placing the receiving antenna outside the atmosphere will allow reception of shorter wavelengths and therefore increase the gain of a given size antenna. Gain is proportional to (diameter/wavelength)^2. The mass of a given size space antenna could be less than that of a ground based antenna of the same size but there are obviously challenges designing, launching and assembling a precision structure of this scale.
3) Similar issues of size apply to the spacecraft's transmission antenna. An inflatable antenna may prove to be the optimum design. There may be significant distortion due to acceleration. You are interested in maximum distance, so presumably there is been a long thrust phase.
An alternative is to deploy and tune the antennae only after the start of the coast phase of the mission. An intriguing option is to use the antennae as a parabolic solar collector to drive a solar thermal rocket while inside the solar system, and then convert it to a high gain communication antenna during coast phase.
4) How much power is available for transmission? RTGs are limited by the lifespan of the isotope: 89 years for 238Pu, 432years for 241Am (with a half life of , but only a fifth the power density of 238Pu). Mass of isotope and shielding becomes a significant factor if you are going for maximum distance.
You could consider a nuclear reactor, but the lifespan of fuel rods, even the highly enriched rods used in submarines, is only about 50 years.
Available power will decrease as the mission progresses, but required power for successful communication will increase.
5) How intermittent is the signal transmission? Storing power for a short burst could produce a much stronger signal than continuous transmission. But power storage in cold interstellar space is a challenge. Batteries and supercapacitors don’t like the cold. Insulation and waste heat from RTG could keep them warm.
Answer: it depends.