Northern crater, does the character path affect which item they pick up?

In Final Fantasy VII, one of the final things you do is to go in the Northern Crater. During it, you have a few points where you are forced to split your team up. Those who go with the main party and those who do not.

When you get to the bottom of the crater, you find a room with all the party members in and sometimes the ones who were not with the main group have an item for you. Does this change depending on the character and the direction they took? Is there an optimal route to send people to gain the better quality items or it it just luck? Does anything else affect which items the other party members pick up?

Based this walkthrough posted on GameFAQs (search for {39} in the walkthrough), the items you receive are dependent on who you send which direction. The walkthrough author recommends the following orders:

• Cloud: Left/Down
• Barret: Left/Up
• Tifa: Right
• Red XIII: Left/Up
• Cait Sith: Left/Down
• Yuffie: Left/Up
• Vincent: Left/Down
• Cid: Left/Up

You then enter the path at the bottom of the screen. I haven't verified this myself personally, but you can always try it and either don't save or use another save slot until you can confirm this gets you the items you want.

Note: Once you have completed your path and enter the room with the rest of the party members for the first time, do NOT talk to any of them. If you do not talk to anyone and continue through other doors in the room, you can actually go back along their paths, grab loot from all of the chests on that path, and still get loot from the party members when you return to the room. This is important because the above orders are intended to get you an extra Mystile, Imperial Guard, Shield Materia, and Counter Materia if you explore and loot all of the paths before talking to anyone else in that room.

In the walkthrough, that Tom posted, it contained the information to answer the rest of the question, in section {AP-4} Tricks. Here is a list of what items each character will normally get depending on the route they take:

The Right Path:

Barret: Guard Source

Tifa: Mythril (Mystile)

Red XIII: Mind Source

Yuffie: Last Elixir (Megalixir)

Cait Sith: Elixir

Vincent: Last Elixir (Megalixir)

Cid: Speed Source

The Left-Upper Path:

Barret: Vaccine

Tifa: Hero Drink

Red XIII: Shield materia

Yuffie: (Command) Counter materia

Cait Sith: Remedy

Vincent: Magic Source

Cid: Imperial Guard

The Left-Down Path:

Barret: Remedy

Tifa: Turbo Ether

Red XIII: Speed Source

Yuffie: Vaccine

Cait Sith: X-Potion

Vincent: Mega-All materia

Cid: Elixir

Note: If Cloud goes right, then any party members going left have a 50/50 chance to give either the left-up or the left-down path's item.