Weakly-split spherical Tits systems in quasi-reductive groups

We will prove that any weakly-split spherical Tits system $(B,N)$ in $G= {\bf G}(k)$ (${\bf G}$ a quasi-reductive $k$-group, such as a connected reductive $k$-group) satisfying some natural conditions is ``standard''. In particular, if ${\bf G}$ is anisotropic over $k$, then such a Tits system is trivial, i.e., $B= G=N$.