  The Split Packing algorithm \cite{splitpacking_ws, splitpackingsoda,
splitpacking} is an offline algorithm that packs a set of circles into
triangles and squares up to critical density. In this paper, we develop an
online alternative to Split Packing to handle an online sequence of insertions
and deletions, where the algorithm is allowed to reallocate circles into new
positions at a cost proportional to their areas. The algorithm can be used to
pack circles into squares and right angled triangles. If only insertions are
considered, our algorithm is also able to pack to critical density, with an
amortised reallocation cost of $O(c\log \frac{1}{c})$ for squares, and
$O(c(1+s^2)\log_{1+s^2}\frac{1}{c})$ for right angled triangles, where $s$ is
the ratio of the lengths of the second shortest side to the shortest side of
the triangle, when inserting a circle of area $c$. When insertions and
deletions are considered, we achieve a packing density of $(1-\epsilon)$ of the
critical density, where $\epsilon>0$ can be made arbitrarily small, with an
amortised reallocation cost of $O(c(1+s^2)\log_{1+s^2}\frac{1}{c} +
c\frac{1}{\epsilon})$.
