  First, inspired by a question of Sibony, we show that in every compact
complex manifold $Y$ with certain Oka property, there exists some entire curve
$f: \mathbb{C}\rightarrow Y$ generating all Nevanlinna/Ahlfors currents on $Y$,
by holomorphic discs $\{f\restriction_{\mathbb{D}(c, r)}\}_{c\in \mathbb{C},
r>0}$. Next, we answer positively a question of Yau, by constructing some
entire curve $g: \mathbb{C}\rightarrow X$ in the product $X:=E_1\times E_2$ of
two elliptic curves $E_1$ and $E_2$, such that by using concentric holomorphic
discs $\{g\restriction_{\mathbb{D}_{ r}}\}_{r>0}$ we can obtain infinitely many
distinct Nevanlinna/Ahlfors currents proportional to the extremal currents of
integration along curves $[\{e_1\}\times E_2]$, $[E_1\times \{e_2\}]$ for all
$e_1\in E_1, e_2\in E_2$ simultaneously. This phenomenon is new, and it shows
tremendous holomorphic flexibility of entire curves in large scale geometry.
