The support are gained if a certain event happens and are fixed since that certain part. But they work exactly as is in Fire Emblem Mystery of Emblem. By this I mean that some support only cause an effect to a character and not to both, but others do.
These effects are activated if the characters are between 3 squares away and affect the hit, evasion, critical and critical evade. The bonus is between 0 and 15. If isn't a bonus in the "Addition" or "Max." that you can get (indicated below) is because can't go up, and if is more than one event, isn't possible to get the second event without getting the first
Example:
- Arkis get +5% on hit, evasion, critical and critical evade if Kreiss is between 3 squares from Arkis.
- The same if Arkis is next to Runan, but Runan doesn't get bonus from Arkis.
| Character |
Obtain from |
Start |
Event to increase the support's bonus |
Addition |
Max. |

Runan |

Holmes |
10% |
- |
- |
- |

Enteh | - |
Event during the third division of groups, in Lazeria. |
+15 |
15% |
 Kreiss |

Runan |
5% |
- |
- |
- |

Arkis |
5% |
- |
- |
- |

Leteena |
15% | - |
- |
- |

Rina |
5% | - |
- |
- |

Arkis |

Runan |
5% |
- |
- |
- |

Kreiss |
5% |
- |
- |
- |

Estelle |
- |
Talk in map 2 |
+4 |
6% |
| At the end of the map 10, if both are in Holmes's group |
+2 |

Rina |
5% |
If you get she and Arkis in the Map 26B |
+10 |
15% |

Garo |

Julia |
- |
Conversation at the end of the map 3.
Choose the first option. |
+15 |
15% |

Holmes |
5% | - |
- |
- |

Sasha |

Runan |
5% |
- |
- |
- |

Kate |
5% | Event during the third division of groups, in Lazeria. |
+5 |
10% |

Raffin |
6% |
- |
- |
- |

Mahter |
- |
Talk in map 4 |
+4 |
4% |

Loffaru |
10% | - |
- |
- |

Holmes |
- |
if Sasha is in Holmes's group. In a random encounter in the Welt Bridge |
+3 |
6% |
| Event during the third division of groups, in Lazeria. |
+3 |

Kate |

Sasha |
10% | - |
- |
- |

Zeek |
- |
Conversation at the end of the map 5 |
+5 |
15% |
| Conversation at the end of the map 7 |
+5 |
| Conversation at the end of the map 17 |
+5 |

Loffaru |
5% | - |
- |
- |
| Character |
Obtain from |
Start |
Event to increase the support's bonus |
Addition |
Max. |

Lee |

Plum |
- |
Conversation at the end of the map 2 |
+5 |
5% |

Ezekiel |

Leteena |
15% | - |
- |
- |

Narron |

Runan |
- |
Conversation at the end of the map 10 if Narron is in Runan's group |
+5 |
5% |

Ruka |

Raquel |
10% | - |
- |
- |

Sasha |
5% |
Conversation at the end of the map 7 |
+5 |
10% |

Raffin |

Sasha |
5% |
- |
- |
- |

Estelle |
8% |
- |
- |
- |

Sharon |
5% |
Conversation at the end of the map 10.
Choose the first option. |
+5 |
10% |

Estelle |

Raffin |
15% | - |
- |
- |

Barts |

Enteh |
8% |
- |
- |
- |

Plum |
5% |
In the map 14 if Plum was kidnapped in the map 10, you must visit the house where she is with Barts |
+5 |
10% |

Enteh |

Runan |
- |
Talk in map 2 |
+5 |
15% |
| Conversation at the end of the map 2 |
+10 |

Maruju |
5% | - |
- |
- |

Meriah |
5% | - |
- |
- |

Rishel |
7% |
- |
- |
- |

Julia |

Garo |
- |
Conversation at the end of the map 3.
Choose the first option. |
+10 |
10% |

Vega |
6% | - |
- |
- |

Shigen |
5% |
Conversation at the end of the map 29 if they are in Holmes's group.
Choose the first option. |
+10 |
15% |

Yoda |
5% |
At the end of the map 30 if Julia is in Holmes's group |
|
- |

Plum |

Barts |
6% | In the map 14 if Plum was kidnapped in the map 10, you must visit the house where she is with Barts |
+5 |
11% |

Enteh |
5% |
- |
- |
- |

Lee |
- |
Conversation at the end of the map 2 |
+5 |
5% |

Holmes |
- |
In the map 14 if Plum was kidnapped in the map 10, you must visit the house where she is with Holmes. If it you enter with Barts, isn't possible to enter with Holmes. |
+5 |
5% |

Lionheart |
- |
If during the second division Plum has the Lan's Mirror, is Dancer, and is with Lionheart in the Holmes's group. Then visit Brahd. |
+10 |
10% |

Mahter |

Sasha |
- |
Talk in map 4 |
+4 |
4% |

Enteh |
10% | - |
- |
- |

Frau |
5% |
- |
- |
- |

Rishel |
- |
During the second division after the map 23. |
+5 |
5% |

Verna |
5% | - |
- |
- |
| Character |
Obtain from |
Start |
Event to increase the support's bonus |
Addition |
Max. |

Vega |

Shigen |
- |
On the map 14, if Shigen and Vega are in when starting the battle, and if after the map 13 you choose the first option when Shigen talks to Krisheena. |
+10 |
10% |

Raquel |

Sasha |
5% |
- |
- |
- |

Ruka |
9% | - |
- |
- |

Roger |
- |
Visit Rachel's house in the map 4 with Ruka |
+5 |
10% |
| Event during the third division of groups, in Lazeria. |
+5 |

Zeek |

Kate |
- |
Conversation at the end of the map 5 |
+5 |
5% |

Maruju |

Enteh |
5% |
Conversation at the end of the map 17 if they are in Runan's group |
+5 |
10% |

Mel |
5% |
- |
- |
- |

Meriah |
- | Event during the third division of groups, in Lazeria. |
+5 |
5% |

Mel |

Roger |
15% | - |
- |
- |

Maruju |
5% | - |
- |
- |

Norton |

Sasha |
5% |
- |
- |
- |

Lionel |
5% | Event during the third division of groups, in Lazeria. |
+5 |
10% |

Kate |
- |
Conversation at the end of the map 10, if Zeek, Kate and Norton are in Runan's group |
+5 |
5% |

Thomas |

Plum |
5% | - |
- |
- |

Barts |
5% | - |
- |
- |

Roger |

Mel |
15% | - |
- |
- |

Xeno |

Yuni |
- |
After the second division of groups, if Xeno and Yuni are in Holmes's group. When you pass through Oaks choose the second option. Although this will make impossible to Attrom and Lyria to increase the support between them. |
+15 |
15% |

Katri |
5% |
Conversation at the end of the map 10, in the Saura Port |
+5 |
10% |

Holmes |
5% | - |
- |
- |

Yuni |

Xeno |
10% | After the second division of groups, if Xeno and Yuni are in Holmes's group. When you pass through Oaks choose the second option. Although this will make impossible to Attrom and Lyria to increase the support between them. |
+5 |
15% |

Katri |
5% |
- |
- |
- |

Lyria |
- |
When you pass through Ligria after the map 15, if Yuni and Lyria are in Holmes's Group. |
+5 |
5% |

Katri |

Xeno |
5% | - |
- |
- |

Yuni |
5% | - |
- |
- |

Holmes |
10% |
Conversation at the end of the map 13 |
+5 |
15% |

Meriah |

Enteh |
5% |
- |
- |
- |

Maruju |
- | Event during the third division of groups, in Lazeria. |
+5 |
5% |

Rishel |
10% |
During the second division of groups, immediately after moving, and if Meriah and Rishel and are in Runan's group. |
+5 |
15% |

Renee |
5% | - |
- |
- |

Narcus |

Mel |
5% | - |
- |
- |

Bud |
5% | - |
- |
- |

Sharon |

Raffin |
10% |
Conversation at the end of the map 10.
Choose the first option. |
+5 |
15% |
| Character |
Obtain from |
Start |
Event to increase the support's bonus |
Addition |
Max. |

Billford |

Sharon |
15% | - |
- |
- |

Mintz |

Rennie |
5% |
If in the map 9 Mintz rescued Rennie
(doesn't matter if you recruit Rennie here or in the map 17) |
+5 |
10% |

Hagaru |
5% | - |
- |
- |

Rennie |

Mintz |
10% | If in the map 9 Mintz rescued Rennie
(doesn't matter if you recruit Rennie here or in the map 17) |
+5 |
15% |

Lionheart |
5% | - |
- |
- |

Holmes |

Runan |
10% |
- |
- |
- |

Katri |
5% |
Event after the third division of groups (on Harfa Fort) |
+10 |
15% |

Shigen |
10% | - |
- |
- |

Attrom |
- |
Conversation at the end of the map 29 |
+5 |
5% |

Shigen |

Julia |
5% | Conversation at the end of the map 29 if they are in Holmes's group.
Choose the first option. |
+10 |
15% |

Vega |
- |
On the map 14, if Shigen and Vega are when starting the battle, and if after the map 13 you choose the first option when Shigen talks to Krisheena. |
+10 |
10% |

Sierra |
10% |
Note: Doesn't matter where Sierra joins, she still have the support |
- |
- |

Krisheena |
- |
Conversation at the end of the map 13.
Choose the first option. |
+4 |
8% |
Conversation at the floor 5 in the Morse Tower,
if Krisheena was revived on a previous visit. |

Yoda |
5% | - |
- |
- |

Samson |

Katrina |
15% |
Note: Katrina is a unit that can't be obtained |
- |
- |

Alicia |

Alfred |
15% | - |
- |
- |

Lionel |

Norton |
5% | Event during the third division of groups, in Lazeria. |
+5 |
10% |

Kate |
- |
|
+5 |
5% |

Attrom |

Katri |
5% |
- |
- |
- |

Lyria |
3% |
After the second division of groups, if you have Lyria and Attrom in Holmes's group. When passing through Oaks choose the first option if you have Xeno and Yuni in this group too, although this will make to Xeno and Yuni impossible to increase theirs support. If you don't have Xeno and Yuni, the other two can still increase theirs support but isn't necessary to choose options |
+5 |
8% |

Renee |
15% | - |
- |
- |

Krisheena |

Shigen |
- |
On the map 14, if Shigen and Vega are when starting the battle, and if after the map 13 you choose the first option when Shigen talks to Krisheena. |
+5 |
15% |
Conversation at the floor 5 in the Morse Tower,
if Krisheena was revived on a previous visit. |
+10 |
| Character |
Obtain from |
Start |
Event to increase the support's bonus |
Addition |
Max. |

Maerhen |

Katri |
15% | - |
- |
- |

Frau |

Sun |
10% |
- |
- |
- |

Katri |
- |
Conversation at the end of the map 15. Mahter and Frau should be in Holmes's group. |
+10 |
10% |

Mahter |
5% |
- |
- |
- |

Verna |
5% | - |
- |
- |

Sun |

Frau |
10% | - |
- |
- |

Lyria |

Attrom |
5% |
After the second division of groups, if you have Lyria and Attrom in Holmes's group. When passing through Oaks choose the first option if you have Xeno and Yuni in this group too, although this will make to Xeno and Yuni impossible to increase theirs support. If you don't have Xeno and Yuni, the other two can still increase theirs support but isn't necessary to choose options |
+5 |
10% |

Yuni |
- | When you pass through Ligria after the map 15, if Yuni and Lyria are in Holmes's Group. |
+5 |
5% |

Shirou |

Lionheart |
10% | - |
- |
- |

Loffaru |

Sasha |
15% | - |
- |
- |

Runan |
- |
Talk in map 19 |
+5 |
5% |

Holmes |
- |
Event during the third division of groups, in Lazeria.
Only if Sasha has the supports with holmes |
+5 |
5% |

Lionheart |

Shirou |
5% |
- |
- |
- |

Renee |
5% | Event during the third division of groups, in Lazeria. |
+10 |
15% |

Plum |
- |
If during the second division Plum has the Lan's Mirror, is Dancer, and is with Lionheart in the Holmes's group. Then visit Brahd. |
+10 |
10% |

Zachariah |

Katri |
15% | - |
- |
- |

Bud |

Rishel |
10% | - |
- |
- |

Narcus |
5% | - |
- |
- |

Rishel |

Enteh |
10% | - |
- |
- |

Bud |
8% |
- |
- |
- |

Meriah |
9% | - |
- |
- |

Mahter |
- | During the second division after the map 23. |
+5 |
5% |

Sierra |

Shigen |
15% | Note: Doesn't matter where Sierra joins, she still have the support |
- |
- |

Rebecca |
Nobody |
- | - |
- |
- |

Leteena |

Kreiss |
15% | - |
- |
- |

Ezekiel |
5% | - |
- |
- |
| Character |
Obtain from |
Start |
Event to increase the support's bonus |
Addition |
Max. |

Rina |

Arkis |
5% | If you get she and Arkis in the Map 26B |
+10 |
15% |

Renee |

Attrom |
10% |
- |
- |
- |

Lionheart |
10% | Event during the third division of groups, in Lazeria. |
+5 |
15% |

Meriah |
5% | - |
- |
- |

Yoda |

Julia |
10% |
At the end of the map 30 if Julia is in Holmes's group |
- |
- |

Shigen |
5% | - |
- |
- |

Hagaru |

Mintz |
5% | - |
- |
- |

Verna |

Neyfa |
15% |
Note: Neyfa is a unit that can't be obtained |
- |
- |

Frau |
5% |
- |
- |
- |

Mahter |
5% | - |
- |
- |

Sennet |
5% | - |
- |
- |

Sennet |

Neyfa |
15% |
Note: Neyfa is a unit that can't be obtained |
- |
- |
 Tia |
5% | - |
- |
- |

Alfred |
 Alicia |
5% |
Talk to Alfred with Alicia in the map 21 |
+5 |
10% |

Mel |
10% |
- |
- |
- |
 Maruju |
10% | - |
- |
- |

Tia |
 Sennet |
5% | - |
- |
- |

Richard |
5% |
Note: Richard is a unit that can't be obtained |
- |
- |