Mega Mass

[LucyR]

A rocky planet the size of Jupiter would sweep up comets and other stuff. It would accumulate a very thick atmosphere, eventually becoming a gas giant much bigger than Jupiter, with a Jupiter sized rocky core. If it swept up enough stuff, nuclear reactions would kick in at the core, and it would become a brown dwarf star.

Only if the additional matter was available. In any case, this doesn't address the issue of the likelihood of a Jupiter-mass rocky planet existing in the first place.

 

[wollery]

A rocky planet the size of Jupiter would sweep up comets and other stuff. It would accumulate a very thick atmosphere, eventually becoming a gas giant much bigger than Jupiter, with a Jupiter sized rocky core. If it swept up enough stuff, nuclear reactions would kick in at the core, and it would become a brown dwarf star.

Wow, I'm not even sure where to begin with this one.

For a start, as LucyR mentioned, the material would have to be there to begin with, and given that Jupiter alone comprises well over half the mass of the solar system I doubt that it would be.

Second, although the planet might be more massive than Jupiter it wouldn't be much bigger, above a certain mass the degeneracy caused by gravity and density makes the increase of size with mass negligible.

Third, having a rocky core means that the planet would not undergo any fusion reactions, the amount of energy required to fuse elements such as iron is only found in supernovae.

Fourth, (and last) if it's got stable fusion reactions then it isn't a Brown Dwarf, that's what makes them different from stars.