Your question is mostly about chords, but the term "relative minor" is about key signatures. I will answer from both perspectives:
"Relative major" and "relative minor" are terms typically used to describe keys with identical key signatures and root notes a minor third apart. So, when we compare C minor and Eb major, the key signature is 3 flats and C and Eb are a minor third apart, so we say C minor is the relative minor of Eb major, or vice versa, that Eb major is the relative major of C minor. Another common example is the
0b/0# natural key signature and the relationship between C major and A minor.
Now, if we compare Ab major to C minor, we can't get too far off the ground since Ab is a major third away from C, not a minor third. However, if we get a little creative we can come up with a logical answer:
Let's consider that both chords come out of the same heptachord (set of 7 notes, a.k.a. key signature). We need the notes Ab, C, Eb, and G, which means the fewest number of flats we can use is going to be 3 (see also: Order of flats). This is convenient, because the relative major of C minor is Eb major, or 3 flats.
Now, the "creative" part is that I'm going to extend our terminology to make use of the diatonic "church modes" (lydian, ionian, mixolydian, dorian, aeolian, etc.), so that we can talk about any keys relative to one another that share the same key signature. Aeolian and minor as terms here are interchangeable, since their key signatures are identical.
In this system, I would say that Ab major triad outlines the relative lydian to C minor, because in our key signature of 3 flats (we've already established that the relative major of C minor is Eb major, or 3 flats), the mode that starts on Ab is the lydian mode.
Sidebar: As another example of how I'd use this terminology, consider the chords G minor and A minor. It is possible to draw a relationship between them in the key signature of F (one flat) by saying the G minor triad outlines the relative dorian of A phrygian, and that the A minor triad outlines the relative phrygian of D dorian. This should work for any two chords that are possible within a single valid key signature.
This, I imagine, is going to be closer to the answer you were really looking for.
When we talk about chords, we don't use the terms "relative minor" or "relative major", instead, we talk about functional relationships. For example, G major is the dominant of C major. C minor is called the submediant of Eb major. In the other direction, Eb major is called the mediant of C minor.
These names, and a much more in-depth explanation can be found on the above linked Wikipedia article. Mediant relationships involve distances of a 3rd.
So then, if we look at the chords in your question (Ab major, C minor, Eb major) and we are in the key of C minor, we would say Ab is the submediant of C minor and Eb is the mediant of C minor.