Earth is 108 times smaller than the sun in terms of its diameter while Jupiter is 10 times. Assuming Jupiter was located such that it could sustain life, theoretically how big a planet can get with respect to its star in order for it sustain life?
There is indeed a limit to size of planets for holding life. For planet habitability, the radius of planet should range between 0.5 and 2.5 Earth radii. (there is a list of exoplanets that are more likely to have a rocky composition and maintain surface liquid water (i.e. 0.5 < RP ≤ 1.5RE or 0.1 < MP ≤ 5ME). Let's look at the limits of the planet size and what happens if the limits are crossed:
[...] the size of the planet places an important constraint on this process. Bigger planets will have more gravity and this determines both the atmospheric pressure and the pressure at the bottom of the oceans. If this is too large, ice will form at the bottom of the oceans preventing liquid water from interacting with the silicate material that makes up the ocean floor. And when that happens, the carbon cycle immediately shuts down leaving the planet at the mercy of any temperature changes.
Alibert goes on to calculate the radius of an Earth-like planet above which a carbon cycle cannot operate. The critical threshold turns out to be about twice the radius of Earth (although this depends on a variety of factors such as the mass, density and make up of the planet). Alibert’s claim is that although there is no guarantee that planets in the habitable zone that are less than twice the radius of Earth will actually be habitable, those that are bigger than this threshold are not habitable.
If a low-mass planet is too small, it won’t have enough gravity, and the atmosphere will be stripped away, and the water will either be stripped away with it, or frozen on the surface. That means the prospects for life are dim. The researchers say there is a critical lower limit for a planet to be habitable. That means that not only is there a band of proximity to the star that determines a planet’s habitability, there’s a size limit.
That critical size, according to Arnscheidt and the other authors of the study, is 2.7 percent the mass of Earth. They say that any smaller than that, and the planet simply won’t be able to hold onto its atmosphere and water long enough for life to appear. For context, the Moon is 1.2 percent of Earth’s mass, and Mercury is 5.53 percent.
There are other parameters like orbit/rotation, geology, surface temperature, magnetosphere, is it located in so called "goldilocks" or habitable zone? etc. that also determine if the exoplanet is suitable for harboring life and when all parameters are taken together then the supposed data of "appropriate planet size for holding life" could change.
Relative sizes don't matter for life, what matters is the correct distance for the correct temperature so that liquid water can exist on a planet's surface. If the Sun became a white dwarf it would be about as big as Venus or Earth. As for how big solid planets (or ocean planets) can get, the biggest known super-Earth is Kepler-10c at 2.35 Earth radii and 7 Earth masses (by comparison Uranus has 14.5 and Neptune 17.1 Earth masses).
Edit: User sno found an even larger planet at 3.36 Earth radii, see his answer.
The Wikipedia article https://en.wikipedia.org/wiki/Mega-Earth lists Kepler-277c as being a mega-earth with a radius of 3.36 Earth radii and a mass of 64.2 Earth masses. It is too close to its star for liquid water but a similarly sized planet could have liquid water if it was further from its star.