constructive meta-kernelization theory on sparse graphs, by enhancing the existing framework [@KviaDP] in order to deal with [*packing*]{} problems. These are problems whose solutions can be certified by collections of [*subgraphs*]{} of the input graph satisfying certain properties. We call these problems *packing-certifiable*, as opposed to *vertex-certifiable* ones. For instance, deciding whether a graph $G$ contains at least $k$ vertex-disjoint cycles is a typical packing-certifiable problem. This problem, called <span style="font-variant:small-caps;">Cycle Packing</span>, is [[FPT]{}]{} as it is minor-closed, but it is unlikely to admit polynomial kernels on general graphs [@BodlaenderTY11].

As an illustrative example, for a family of connected graphs ${\mathcal F}$ containing at least one planar graph, we provide a linear kernel on sparse graphs for the <span style="font-variant:small-caps;">${\mathcal F}$-Packing</span> problem[^4]: decide whether a graph $G$ contains at least $k$ vertex-disjoint subgraphs such that each of them contains a graph in ${\mathcal F}$ as a minor, parameterized by $k$. We provide linear kernels as well for the following two [*orthogonal generalizations*]{} of ${\mathcal F}$-<span style="font-variant:small-caps;">Packing</span>: for an integer $\ell {\geqslant}1$, one aims at finding either minor-models that are pairwise at distance at least $\ell$ in $G$ (<span style="font-variant:small-caps;">$\ell$-${\mathcal}{F}$-Packing</span>), or such that each vertex in $G$ belongs to at most 