How much bigger can an LR(1) automaton for a language be than the corresponding LR(0) automaton?
The grammar

$$\begin{array}{l}
S \rightarrow T_0 \\
T_n \rightarrow a \; T_{n+1} \\
T_n \rightarrow b \; T_{n+1} \\
T_n \rightarrow b \; T_{n+1} \; t_n \\
T_N \rightarrow t_N
\end{array}
$$

has the LR(0) state
$$T_N \rightarrow t_N \dot \\$$
expanded to $2^N$ variants in the LR(1) automata as all the partitions of $\{t_0 \dots t_{N-1}\}$ are possible look-head which appear in different contexts.  The number of states in the LR(0) automaton on the other hand is linear in term of $N$.  Thus an expansion factor of the order of $2^N/N$ is possible.

Edit: I'll have to check later when I've more time, I think adding $T_N \rightarrow T_0$ would give the exponential factor on nearly all the LR(0) states. That result in a shift-reduce conflict.