This is a list of the possible Summons Screens that can be displayed when performing Summons. They do not affect the results in any way - quite the opposite, it's the result of the Summon that affects the animation - but some of these animations are able to reveal whether you pulled at least one character or not.
Update: as of May 24th, 2018, all Multi-Summons performed with Dragon Stones now guarantee an character in the 10th slot.
Update: as of June 25th, 2018, the Japanese version of the game has different animations as a result of the 3.13.0 update.
"Bye, Guys" is a rare summon animation which guarantees a character of rarity.
"It's Over!!!! Freeza!!!" is an old animation screen which occasionally popped up guaranteeing a character of rarity. The animation was removed but was later brought back when the game was updated to version 3.10. The animation now guarantees rarity pulls.
"Thank You Dragon Balls!" is a rare summon screen which is similar to "Bye, Guys". It will guarantee an character.
Saiyan Pods are random animations during summoning. Anywhere from 0-7 pods may appear during summons. 7-pod summons guarantee an rarity character (which is usually a Hercule Statue in Friend Summons, or an SR character Z-Awakened to SSR).
Hercule is another random animation that may appear if Saiyan Pods do not appear. Hercule may appear on the right or left side. Hercule does not have a direct effect on the rarity of a pull, but it is speculated that Hercule on the left side usually equals a higher rarity card.
Shenron is a very rare animation (the chance for it to appear is only 0.12%). It guarantees an rarity character.
A rainbow release means that there's an increased chance to pull a featured character from the scouter display. If Goku stays in his base form after a rainbow release, it's guaranteed to shatter the screen for an rarity card.
If Goku transforms only to Super Saiyan, then this is generally only an rarity character, however, there is a rare chance to result in a shattered screen.
If Goku transforms to Super Saiyan 2 during a summon, it guarantees a character of the rarity, although it can also be an rarity character.
If Goku transforms to Super Saiyan 3 during a summon, it guarantees an rarity character.
A beeping scouter indicates that a character of the rarity is present. This will not always occur with all characters.
"Give Me Girl Panties!!!!!" is a summon animation that can appear after "Bye, Guys" or any of the other animations, by shattering the screen a second time. As far as we know, it guarantees an or a character.
Before the Kamehameha blast, a number of different Z-Fighters may fly alongside Goku.
It looks like an or a character might be guaranteed whenever Majin Buu shows up while carrying Hercule on his back.
On some occasions, it's possible that Goku will not ascend to Super Saiyan. Unless it's a multi-summon, the pull will likely be an . There is, however, a rare chance for a shattered screen, producing an instead.
Occasionally, the text during a summon will have a rainbow color rather than the default yellow. Rainbow text means a higher possibility of a featured unit being in the summon. If Goku does not ascend and the text is rainbow, it is a guaranteed shattered screen.
If Goku ascends only to Super Saiyan during a summon, at least one character is guaranteed. However, there is a rare chance to result in a shattered screen or an .
Goku may also ascend to Super Saiyan 2. This animation guarantees at least one , but like SS1, can give an .
If Goku ascends to Super Saiyan 3 during a summon, it guarantees an character.
If Goku ascends past Super Saiyan 3, he will turn into Super Saiyan God. This animation guarantees 3 characters.
Goku can ascend to Super Saiyan Blue Kaioken as a step above SSG, and most likely guarantees either an or a . However, this animation is currently unobtainable, and is only in the game files.
If Vegeta is flying alongside Goku before the Kamehameha blast, they'll have a chance to fuse into either Super Vegito or Vegito Blue. Super Vegito indicates that you're going to get either an or a character.
This animation guarantees an .
The following silhouettes of characters have a chance of being replaced by an or a character:
When summoning a character that can be Dokkan Awakened to , the LR icon will appear over the card. Once the summon is over, the card will be highlighted and the following text will appear: