Are skins profile wide?

Say I unlock a Zero skin from my Maya character.

If I load up my Zero character from the same profile, does he still get it?

Or if I unlock a Zero skin on my Zero character and then create a second Zero. Is that skin still available to the second character?

If you unlock a Zer0 Skin, while playing Maya, Zer0 will have that skin available in the Quick Change station on the same profile.

EDIT: Note that certain Heads and Skins, in particular the Community Day heads and skins, are account bound and will disappear if not used before quitting BL2. I am not sure if they still drop, but if they do you need to “use it or lose it”. I found that out the hard way (a while ago), when I found one of the Krieg Community day items and stored it in Claptrap’s stash. It was gone the next time I loaded BL2.

Forum ID: Poisd2Strike
GT: Poisd2Strike
Trades: http://forums.gearboxsoftware.com/t/poisd2strikes-humble-shop/367700
Gun Prefixes | Gun Parts | Max Stats
Maya OP8 | Banshee RR / NRR | Binder | Cat | Nurse | Siren | Trickster B / M

Yes, all skins and heads are associated with your profile, not a particular character save associated with that profile. You do have to “use” them from within your inventory before they’ll show up for the relevant character at a quick change station, though. Wish I’d known this when I started, as I dropped or sold a lot of skins/heads when I realised they weren’t for the character I was playing.