Electronic – H-Bridge out of 2 (1 PNP, 1 NPN) Darlington Arrays

One approach would be to control N relays using N+1 half-H-bridges. One of them connects to one wire which is common to all the relays, and the others connect to one relay each. A variation on this would be to arrange the relays into a matrix, with a half-H driver for each row or column (the N+1-half-bridge solution is simply a 1xN matrix). One caveat with this approach is that other relays--especially those in the same row or column as the driven relays may receive a substantial fraction of the drive voltage. In an NxN matrix, the voltage fraction will be (N-1)/(2N-1), which would be 1/3 for a 2x2 matrix, 2/5 for a 3x3 matrix, and would approach 50% as a matrix got bigger. For a non-square matrix, things would be worse.

If you can be sure that relays will not fire unless they receive more than half the rated drive voltage, a square matrix approach might work. Even the relays which don't fire would gobble significant current (as the matrix gets bigger, the voltage across the relays in the same row and column as the driven row would approach half the drive voltage, so figure current similarly); if one used an 8x8 matrix, the total current gobbled by the inadvertently-driven relays would be about 7x the current going to the deliberately-driven one. Not great, but being able to drive 64 relays with 16 half-bridge drivers might be worth it.

An NPN darlington can be made with the collectors of the two NPNs connected together. In transistor technology, this is the substrate (basically the starting point for the transistor construction). Sharing the collectors allows relatively cheap construction. Basically, the transistor is constructed from a 'holder' layer that is the collector; separate bases are constructed simultaneously in this, and separate emitters are constructed simultaneously in each of these;

A composite darlington (Szilaki) requires more complex construction with the PNP's base needing to be distinct from the NPN's collector (or emitter) structures.

In an IC, there are already many different semiconductor layers (for constructing these PNPs and NPNs), so the structures are already available.