Note: this is not a complete answer.
The shape depends on the species.
The "Lost Middle" is not common, but few grasses do it: plant expands on outer border, but in the middle there remain the old tuft and roots, which prevent new plants. This is usually on perennials with very short runners (practically no real runner). In such case there is just one method: remove all, cut one piece and plant it again in center (possibly replacing soil). Note: the central roots are still used by the lateral runners, so it is not really "dead leaves" which prevent growth, but the plant itself. On the other hand, you may cut it our so to force the new root to be fully developed and used.
Lost shape is normal. If plants see a new good place, they try to expand and conquer new territory. Just remove the satellites one or twice per year, check soil (make them less ideal), check irrigation (not to water such zone). Usually perennials, possibly with some runners.
Lost shape #2 is also very common on perennial grasses to have runners, but this is not ideal on your case, but good if one want to cover a rooftop, or a irregular (and with a lot of rocks/concrete) surface. If you want shape, do no plant grasses with many runners.
Your ideal case: some perennials do it: no runners. They will just try to go to new places with seeds. But in this case you should replace it from time to time, to remove the old parts. Many of such plants are slow and possibly not very ornamental.
For completeness: many grasses are annuals, so they cannot keep a shape, and usually not very tuftous and ornamental.
I would just cut the part out of shape, and replant them every few years to avoid void middle, and to give them new soils, so new strength.
But for true answer, one need to know the exact species and the terrain.