Mapping the Milky Way with LAMOST III: Complicated spatial structure in the outer disc

We present {complexity} of the Galactic outer disc {by fitting the stellar volume densities of the red giant branch stars with a two-disc component model}. {The discs are confirmed to} extend to $R\sim19$\,kpc. The radial density profile of the discs shows {two breaks at $R\sim11$ and $\sim14$\,kpc, respectively, which} separate the radial profile into three segments with different scale lengths of $2.12\pm0.26$, $1.18\pm0.08$, and $2.72$\,kpc at $R<11$, $11\leq R\leq14$, and $R>14$\,kpc, respectively. The first {break} is likely due to the sudden drop in the radial profile of the thin disc, which may be an evidence of the radial migration. {Beyond $14$\,kpc, the thick disc becomes prominent and the transition from thin to thick disc leads to the second break.} This implies that the geometrically defined thick disc is more {radially} extended than the thin disc. This is also supported by the larger scale length of the thick disc than that of the thin disc. Meanwhile, {the scale height of the thicker component increases from $0.637_{-0.036}^{+0.056}$ at $R=8$ to $1.284_{-0.079}^{+0.086}$\,kpc at $R=19$\,kpc, showing an intensive flared disc}. Moreover, rich substructures are displayed in the residuals of the stellar density. Among them, the substructures $D14+2.0$ and $O14-1.5$ show a north-south asymmetry, which can be essentially explained by southward shifting of the thick disc. However, no significant overdensity is found for the Monoceros ring. Finally, the thick disc shows a ripple-like feature with unclear origin at $9<R<10.5$\,kpc.