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Could anyone clarify this for me:

Do parties need Horizontal + Vertical Privity to be in privity of estate?

I understand horizontal privity = burden runs & vertical privity = benefit runs

But does one need both horizontal + vertical privity to be in privity of estate?

Very confused right now ...

1. Horizontal privity and vertical privity are sub-types of privity of estate. Being in privity of estate could mean being in vertical privity or horizontal privity or both.

2. Here's a chart from our class that might prove useful regarding covenants: Traditional rule
  Horiz Priv Vert Priv
BurdenYes (grantor/grantee or L-T) Yes – successor must have same estate as original promisor for burden to run
Benefit No Yes – successor must have some interest succeeded from original promisee. (Yes for lessee, no for adverse possessor)

Note: Restatement Third does away with the privity requirement and instead focuses on whether or not the covenants may be voided by any public policy or countervailing interests but otherwise enforces.

That was quick, but I think it's at least 82% correct.

Horizontal and Vertical privity are terms we only learned for covenants. But yeah for the burden of a covenant to run the majority rule is that you need both. For the benefit to run you only need vertical. Think of it like needing standing to sue. Courts don't really want strangers being able to enforce covenants. Think about it functionally and maybe it will make more sense.

For assignment and sublease we talked about privity of estate as opposed to privity of contract, but not the vertical/horizontal distinction.