  In 1956, 48 years after Hausdorff provided a comprehensive account on ordered
sets and defined the notion of a scattered order, Erd\H{o}s and Rado founded
the partition calculus in a seminal paper. The present paper gives an account
of investigations into generalisations of scattered linear orders and their
partition relations for both singletons and pairs. It provides analogues of the
Milner-Rado paradox for these orders instead of ordinals. For infinite, regular
$\kappa$, we investigate the extent to which the classes of $\kappa$-scattered,
weakly $\kappa$-scattered, and $\kappa$-saturated linear orders of size
$\kappa$ are closed under the partition relation $\tau \rightarrow (\varphi,
n)^2$ for all $n < \omega$. We prove that for a regular cardinal $\kappa$ such
that the stick principle holds at $\kappa$ and $\mathfrak{b}_\kappa =
\kappa^+$, the partition relation $\kappa^+\kappa \rightarrow (\kappa^+\kappa,
3)^2$ fails.
  Finally we generalise a result of Komj\'{a}th and Shelah about partitions of
scattered linear orders to a similar result about partitions of
$\kappa$-scattered linear orders for uncountable $\kappa$. Together this
continues older research by Erd\H{o}s, Galvin, Hajnal, Larson and Takahashi and
more recent investigations by Abraham, Bonnet, Cummings, D\v{z}amonja,
Komj\'{a}th, Shelah and Thompson.
