you know, as much impact as ubuntu has on debian, i think its quite expected to think that debian might be based on ubuntu than the other way around. They do have the chops after all. Just thought it worth making that point. Sytemd is a great example. Devuan has forked off of debian because of ubuntus influence in this area as i understand it.
It's a two-way co-op. Ubuntu uses Debian's packages and repackages them as their own (plus some patches) and in return they give those patches back to Debian. The co-op also works in architectural areas (like choosing systemd), although it was the Debian's Technical Commitee that chose systemd as a sysinitv replacement (I was following the voting process on the mailing lists). It's a win-win scenario, as Ubuntu, being the more popular distro and having even more popular forks like Mint handles a lot of bug reports. The fixes after some time get propagated to Debian. A good example would be grub-commons and it's code for adding a suffix in the Linux menu entries (either "Linux" or "GNU/Linux"): the list for non-GNU entries includes Ubuntu, Kubuntu and other *buntus (and we're talking about the Debian's version of the package).
Sparky's relation to Debian is similar to Ubuntu's, but we don't repackage the whole world (it's a lot of work and a lot of resources would be needed; a single arch repository has a size of about 120GB and we use two archs: x86 and AMD64, so imagine hosting that monster). We use Debian's repositories directly and override any packages we need in our own repos.