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The latter.
Dorrinal's answer to your query on the WW VTES forum is correct.
See the rulebook for confirmation. "The advancement and the base card are
treated as a single vampire card, even if sent to the uncontrolled region
somehow, until the vampire is burned." [1.5.6]
--
LSJ (vte...@white-wolf.com) V:TES Net.Rep for White Wolf, Inc.
Links to V:TES news, rules, cards, utilities, and tournament calendar:
http://www.white-wolf.com/vtes/