The correct statements among I to lII regarding group 13 element oxides are, 

(I) Boron trioxide is acidic oxide. 

(II) Oxides of aluminum and gallium are amphoteric. 

(III) Oxides of indium and thallium are basic.

Acidic oxide is the one that forms acid or make solution acidic on addition of water. Boron trioxide is acidic oxide as it forms boric acid when reacts with water.

${\mathrm{B}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\mathrm{O}\to 2\mathrm{B}{\left(\mathrm{OH}\right)}_3$

Al₂O₃ is amphoteric oxide because it reacts with both base and acid.

$\begin{array}{ccc}{\mathrm{Al}}_2{\mathrm{O}}_3+6\mathrm{HCl}& \to & 2{\mathrm{AlCl}}_3+3{\mathrm{H}}_2\mathrm{O}\\ {\mathrm{Al}}_2{\mathrm{O}}_3+2\mathrm{NaOH}+3{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{NaAl}{\left(\mathrm{OH}\right)}_4\end{array}$

Gallium oxide is amphoteric because it reacts with both acid and base.

$\begin{array}{ccc}{\mathrm{Ga}}_2{\mathrm{O}}_3+2\mathrm{NaOH}+3{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{Na}\left[\mathrm{Ga}{\left(\mathrm{OH}\right)}_4\right]\\ {\mathrm{Ga}}_2{\mathrm{O}}_3+6\mathrm{HCl}& \to & 2{\mathrm{GaCl}}_3+3{\mathrm{H}}_2\mathrm{O}\end{array}$

Basic oxide are those that form base when reacts with water. Indium and thallium are basic oxide as they form base when reacts with water.

$\begin{array}{ccc}{\mathrm{In}}_2{\mathrm{O}}_3+3{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{In}{\left(\mathrm{OH}\right)}_3\\ {\mathrm{Tl}}_2\mathrm{O}+{\mathrm{H}}_2\mathrm{O}& \to & 2\mathrm{TlOH}\end{array}$