Let $X_1\ldots,X_n, n \geq 1$, be independent, identically
distributed random variables and consider the Student $t$-statistic $T_n$ based
upon these random variables. Giné, Götze and Mason (1997) proved
that $T_n$ converges in distribution to a standard normal random variable if
and only if $X$ is in the domain of attraction of a normal random variable
and$EX = 0$. We shall show that roughly the same holds true for the
bootstrapped Student $t$- statistic $T_n^*$. In the process we shall disclose
all the possible subsequential limiting laws of $T_^*n$. The proofs introduce a
number of amusing tricks that may be of independent interest.