What determines whether an aldol reaction will occur again or eliminate?
Partially yes. The big problem with aldol reactions in general is that there are a lot of species that can react together to form stable compounds resulting in low yield. There are numerous ways to counter this:


Specific enolate equivalants, like lithium enolates, silyl enol ethers, aza enolates, enamines, etc. These are among the most important.
Lack of proton in $\alpha$-position.
Strong thermodynamic favoring of certain products in combination with reversibility of the reaction.
etc.


As for your example the $\beta$-hydroxy ketone is more sterically hindered than acetone and is therefore not very likely to be the major contributor (although polymerization can still happen of course).

In general you cannot predict whether or not elimination of $\ce{H2O}$ occurs after the aldol reaction, but the likeliness can be increased by forcing certain reaction conditions.