Do partitions on SSDs map to physical addresses?

One of the reasons that some folk partition hard drives is that certain parts of the hard drive are supposed to be faster than others. Considering that HDDs are a serial access medium, partitioning, in addition to creating logical partitions, also map to a particular physical set of clusters/blocks on the hard drives

Now, with SSDs, its a whole different ballgame - wear leveling would rely on data being writable anywhere on disk, and with serial access, fragmentation has less of an effect

So.. do partitions on SSDs correlate to physical sectors on a disk like HDDs, or is it abstracted away at a higher level?

In order to know this, you should check how wear leveling works.

Where do writes to a specific partition go?

In both dynamic and static wear leveling, a map is used to link Logical Block Addresses (LBAs) to the SSD memory. Thus, any write that you do to the SSD can get placed anywhere on the SSD...

You can see it as some kind of extra interface between your OS and your SSD, which just translates locations into other locations. Towards the OS there is just no difference. However, if you were able to look past the map you would see a lot of data scattered around, like a really fragmented disk!

What will prevent that I write more than the partition can contain?

The OS does this, as a partition only has a limited amount of LBAs.