  We consider various notions of holomorphic extendability of complex valued
functions defined on subsets of $\mathbf C^n$, including one-sided
extendability. We show that in the relevant function spaces, these phenomena of
holomorphic extendability are rare in the topological sense, generalizing
several results of the article "One sided extendability and $p$-continuous
analytic capacities" by E. Bolkas, V. Nestoridis, C. Panagiotis and M.
Papadimitrakis, in dimensions $n\ge 2$.
