There are a few ways to manipulate screen transitions:
The inertia of the Link moving over ice makes him move during the screen transition, affecting the final position by a few tiles.
The color of the Links is of importance, because it causes different results, including a potential softlock.
*Rolling gives you more speed, hence more distance, but a Jump Slash, or probably just walking will also have an effect.
Using other combinations won't do anything or might softlock the game, because it puts the Links into a state where they keep walking in place, while one Link is moving away from them. The stuck Links can still receive damage though, but wont die. Only the distant Link will die, and can then move around. If he gets close to the others, or crosses their X/Y axis (depending on the situation), the Links will revive, nullifying the "softlock".
Since you need ice tiles to perform this, the usage is extremely limited, and restricted to 7-1, 7-2, 7-3 and one screen of the tower collapse.
It is used in 7-1 to obtain the Blue Bracelet early, and to skip the Jewel Fight.
In 8-2, there are a few screen transitions at the beginning where all Links must stand on a cloud to trigger the transition. If a respawning non-Green Link triggers the transition, you can reunite and screw up the coordinates given on the next screen.
The only use so far is to skip Bombs in 8-2 without going through the GBA sections.
Softlock for documentation's sake:
Sometimes the game locks the screen so the player is incapable of leaving until a certain goal has been accomplished. However, you can throw a medallion which will nullify this lock and makes it able to exit the screen. This is used to skip the Jewel Fight in 7-1.