This paper shows how finite approximations of long distance dependency (LDD) resolution can be obtained automatically for wide-coverage, robust, probabilistic Lexical-Functional Grammar (LFG) resources acquired from treebanks. We extract LFG subcategorisation frames and paths linking LDD reentrancies from f-structures generated automatically for the Penn-II treebank trees and use them in an LDD resolution algorithm to parse new text. Unlike (Collins, 1999; Johnson, 2000), in our approach resolution of LDDs is done at f-structure (attribute-value structure representations of basic predicate-argument or dependency structure) without empty productions, traces and coindexation in CFG parse trees. Currently our best automatically induced grammars achieve 80.97% f-score for f-structures parsing section 23 of the WSJ part of the Penn-II treebank and evaluating against the DCU 1051 and 80.24% against the PARC 700 Dependency Bank (King et al., 2003), performing at the same or a slightly better level than state-of-the-art hand-crafted grammars (Kaplan et al., 2004).