A press release on the new Porsche turbo and one of the new technologies listed was a variable displacement oil pump to reduce parasitic torque at high rpms.
I Googled a bit but could not find any info on how it works. There is mention of axially displacing gears in the press release.
There are a couple of variations.  The ones I know of (from working at a Tier-1 engine oil- and transmission pump supplier) are of the vane or gerotor type where the eccentricity between inner and outer elements are varied using a hydraulic feedback and a pressure control valve.  More eccentricity greater flow/pressure and vice versa.  The center rotor is usually fixed and is the driving element while the outer is allowed to move about a pivot axis. At least some of the single-coupling Hydramatic transmissions (very early 50's) had variable displacement front pumps. The vane housing slid to vary the displacement. It could fail, jam at full displacement, and prevent upshift from 2nd to 3rd.

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