The anchor points are selected with the first and 3rd arguments to \stackinset
. The 1st argument is the horizontal anchor, l
eft, c
enter, or r
ight, while the 3rd argument is the vertical anchor, t
op, c
enter, or b
ottom. The 2nd and 4th arguments provide offsets for the anchors if you don't want them precisely at the left, center, or right, etc.
The anchor point of the \rotatebox
plays a role too, and the one complicating factor is if the vertical position of the anchor point changes in the middle of the nested insets. Fortunately, for the two examples you requested, that did not play a role.
\documentclass{article}
\usepackage{stackengine,graphicx}
\begin{document}
\sffamily
\stackinset{l}{}{b}{}{\rotatebox[origin=left]{15}{Blume}}{%
\stackinset{l}{}{b}{}{\rotatebox[origin=left]{30}{Blume}}{%
\stackinset{l}{}{b}{}{\rotatebox[origin=left]{45}{Blume}}{%
\stackinset{l}{}{b}{}{\rotatebox[origin=left]{60}{Blume}}{%
Blume%
}}}}
\stackinset{c}{}{c}{}{\rotatebox{20}{Blume}}{%
\stackinset{c}{}{c}{}{\rotatebox{40}{Blume}}{%
\stackinset{c}{}{c}{}{\rotatebox{60}{Blume}}{%
\stackinset{c}{}{c}{}{\rotatebox{80}{Blume}}{%
Blume%
}}}}
\end{document}
