With the full genome of a 6700 year old male aurochs being sequenced since 2013, it is possible to get better insight on the genetic relationships between wild aurochs populations and domestic cattle, if there was local introgression from wild individuals and which genome regions were particularly influenced by domestication. Now a summary of some recent papers.
The whole-genome sequencing data placed this British aurochs as an outgroup to all modern European cattle [1,2]. mtDNA suggested that Southern European and North-Central European aurochs formed different genetic groups, the latter one being closer to domestic cattle than North-Central European aurochs are . Perhaps hence the genetic distance of the British aurochs, but I tend to think that a southern European aurochs would be an outgroup to cattle as well.
Nevertheless, it seems confirmed that farmers did consciously breed wild aurochs into their stock. Orlando 2015 found that British cattle breeds (in particular: Highland, Dexter, Welsh Black, Kerry, White Park ) show substantial amount of admixture with British aurochs, sharing many polymorphisms . This suggests that Neolithic farmers consciously bred aurochs into their stock, perhaps to gain local climatic and immunologic adaptions for their cattle (those which, after all, originated in the Near East) [1,2].
Orlando 2015 concluded: „Most European breeds apparently developed in situ with no mitochondrial influence from local aurochs, except perhaps Italy, Poland and Switzerland where B. primigenius mtDNA variants can be occasionally found in modern and/or ancient cattle. “
The case from Switzerland that he mentioned is described in a 2014 paper that reported the skeleton of a small female bovine standing only about 1,10 meters high at the withers, therefore being undoubtedly a domestic cow, dated to 5300-5000 years BP, but possessed a mtDNA P-haplotype variant of the European aurochs. Therefore this individual is the result of local admixture – and further not a first-generation hybrid because of its size. It again suggests intentional breeding with (female) aurochs . According to Park et al. 2015, the Q haplogroup suggests limited local admixture as well . It is important to note that no modern domestic cattle have the P mtDNA haplotype, which does not imply that all the nuclear genes introduced by the interbreeding were lost as well, as long the lineage did not vanish.
So now we have it confirmed that local aurochs did leave a genetic trace in European domestic cattle. Evidence indicates that it happened only rarely, but in my opinion this kind of evidence and the material we have is not able to determine the quantity of such events.
However, I see no reason to be euphoric over the results and draw conclusions like Italian or British cattle being more of an European aurochs than other cattle.
An interesting side note: Park et al. 2015 detected traces of zebuine components in some Italian cattle (Chianina, Marchigiana and Romagnola) and East Asian cattle (Hanwoo and Wagyu). But it is also possible that those are alleles that other taurine cattle have lost .
It was found that domestication affected genes for neurobiology, growth, muscle development, metabolism and immunology .
Last but not least, an interesting passage from Orlando 2015 that brings up some aspects of domestication that might not be that often considered:
„Animal domestication is, however, likely to not just have remodeled the sequence of the
genome. Micro- biomes, for example, might also have changed in relation with dietary
shifts, which possibly affected important phenotypic traits, ranging from the physiological
to the behavioral. As wild and domestic animals show subtle changes in brain gene
expression networks, transcrip- tional changes are also likely to have been an early
component of domestication.“
 Orlando, L.: First aurochs genome reveals the breeding history of British and European cattle, 2015.
 Park et al.: Genome sequencing of the extinct Eurasian wild aurochs, Bos primigenius, illuminates the phylogeography and evolution of cattle. 2015.
 Lari et al.: The complete Mitochondrial genome of an 11,450-year-old Auerochsen (Bos primigenius) from Central Italy. 2011.
 Schibler, Elsner & Schlumbaum.: Incorporation of aurochs into a cattle herd in Neolithic Europe: single event or breeding? 2014.