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Many Improved Familiars (e.g. ratling, imp, faerie dragon) have spell like abilities (SLAs). In each's default monster listing, it lists a caster level (CL) for them, e.g. (from ratling)

Spell-Like Abilities (CL 6th; concentration +7)

Familiar Basics changes a number of things for creatures that become familiars, including

Hit Dice: For the purpose of effects related to number of Hit Dice, use the master's character level or the familiar's normal HD total, whichever is higher.

Does this increased HD get used as the CL for the familiar's SLAs? Or does the CL always stay whatever's listed in the familiar's default stat block?

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No, Familiar HD and CL do not increase.

The 'effects' referenced in your quote are actually spells that would target it like Sleep. For the purpose of abilities, the rule

It retains the appearance, Hit Dice, base attack bonus, base save bonuses, skills, and feats of the normal animal it once was, but is now a magical beast for the purpose of effects that depend on its type.

supersedes the other. It's HD are static and unlike Animal Companions, it does not gain more HD or anything of the like from its master's EWL.

I will clarify that these are RAI, and this is a highly debated issue that it seems like Paizo will errata at some point. See my related post answer for a more in-depth response and the quote from a Paizo Contributor that this is based on. A GM could easily decide either way with it, but I will leave you with the point that this Reddit post shows some of the dangers of allowing Familiars to use their master's HD for DC calculations.

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Caster Level Is Not Always Hit Dice

According to the Universal Monster Rules on Spell-like Abilities, the familiar's CL would only change if the ability in question had no listed CL

... If no caster level is specified, the caster level is equal to the creature's Hit Dice...

This means that the very few spell-like abilities that don't specify CL could have their CL improved to the master's HD. For other effects related to HD, such as word of chaos, would indeed be calculated by the master's HD when the master's are higher (sometimes this might be detrimental...oh well).

Other than spells like word of chaos, I'm finding very few abilities or effects that don't say 'racial HD' when using HD for calculations, and the 'phantom HD' from the master's level may or may not be considered racial HD. They don't say that they are, so they most likely are not, but RHD are the only type the familiar is likely to have. It appears to be unmentioned in the rules, however.

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  • \$\begingroup\$ I would venture to say that what you deem 'phantom HD' are definitely not racial HD- if you look at modifying creatures, very little (except explicitly adding racial HD) modify the racial HD because it is generally static. \$\endgroup\$ – Ifusaso Aug 29 '16 at 15:56
  • \$\begingroup\$ Wow, I wasn't quite as clear as I'd meant to be. Fixing. \$\endgroup\$ – Chemus Aug 30 '16 at 0:30
  • \$\begingroup\$ Clarity improved, I actually meant that to read that you stated a good point. More clarity. \$\endgroup\$ – Ifusaso Aug 30 '16 at 13:02
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While unable to find anything that says yay or nay conclusively, the SLAs of a Gnome are tied to his character level. As PCs have character level = Hit dice(Level adjustment not-withstanding), and since Familiars have increased HD, I would strongly believe so.

In addition, http://paizo.com/threads/rzs2onib?Improved-Familiar-SLAs-Caster-Level, agrees with the interpretation that increased HD for familiars increases CL.

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