Familiar's & Master's skills

[Ridley's Cohort]

What exactly does it mean that a familiar may use the master's skills? What bonuses do and don't transfer over?

PHB p. 51: "Skills: Use the normal skills for an animal of that type or the master's, whichever are better."

Suppose I have a Wizard with a Spot skill of:
+6 Ranks +1 Wis +2 Unnamed (Alertness from Familiar) +5 Circumstance (Eyes of the Eagle) +1 Luck (Luckstone) = +15

Is my Wizard's skill a +15 for the Familiar? A +7? Somewhere in between?

To make things more interesting, suppose I have a Bat Familiar. From Tome & Blood, we see the Bat has +3 Ranks +2 Wis +4 Unnamed Racial bonus (when using its Blindsight) = +9

If the Bat uses my Wizard's skill, does he still get the +4 bonus on top of that for using Blindsight?

My intuition says...
(0) Ranks and Wis of Master transfer over, obviously.
(1) Circumstance bonuses never transfer over.
(2) If the Wiz has Skill Focus, it seems natural that the Familiar gains the benefit as much as any ranks. So Alertness does transfer.
(3) Luck bonuses? Competence bonuses? Really not sure. I am leaning towards "yes". Competence bonuses one "better", so that seems like it is part of the skill*. Luck is a little fishy to me.
(4) The Bat does get to add on its +4 Unnamed bonus for Blindsight after choosing to use either its Master's or its own skill. This should be true because the Bat has two distinct Spot skills, based on whether it is in a Silence zone or not.

*I am ignoring for the moment the fact that most Competence bonuses come from using tools. Theorectically, I could have, say, a Ring of Spotting that gives a Competence bonus.

 

[Henrix]

I say only the ranks transfer, provided they are higher. Other modifiers are the familiars.
Oh, and I grant the familiar Alertness from the master.

This is also the way they describe it in T&B, I see when I look it up.

 

[Ridley's Cohort]

Oh! Let me dig that up...

Tome and Blood, page 11: "Skills: The familiar can use its own skills, plus your skills if [sic] is physically able to do so .... To calculate the familiar's score when using one of your skills, use your skill ranks and the familiar's relavant ability modifier. If you both have the same skill and the familiar's score is higher than the score it gets using [sic] your ranks, it can use its own, higher score."

I would agree with you, Henrix.

The text mentions skill ranks, but I think Skill Focus/Alertness should be fair game, too.

Other bonuses would not apply. That prevents a lot of abusive double counting.