(Abridged) In the last decade several massive molecular gas reservoirs were found <100 kpc distance from active galactic nuclei (AGNs), residing in gas-rich companion galaxies. The study of AGN-gas-rich companion systems opens the opportunity to determine whether the stellar mass of massive local galaxies was formed in their host after a merger event or outside of their host galaxy in a close starbursting companion and later incorporated via mergers. We study the quasar-companion galaxy system of SMM J04135+10277 (z=2.84) and investigate the expected frequency of quasar-starburst galaxy pairs at high redshift using a cosmological galaxy formation model. We use archive data and new APEX ArTeMiS data to construct and model the spectral energy distribution of SMM J04135. We also carry out a comprehensive analysis of the cosmological galaxy formation model GALFORM with the aim of characterising how typical the system of SMM J04135 is and whether quasar-star-forming galaxy pairs may constitute an important stage in galaxy evolution. The companion galaxy of SMM J04135 is a heavily dust-obscured starburst galaxy with a median star formation rate (SFR) of $700,rm{M_{odot},yr^{-1}}$, median dust mass of $5.1times 10^9,rm{M_{odot}}$ and median dust luminosity of $textrm 9.3 times 10^{12},rm{L_{odot}}$. Our simulations, performed at z=2.8, suggest that SMM J04135 is not unique. In fact, at a distance of <100 kpc, 22% of our simulated quasar sample have at least one companion galaxy of a stellar mass $>10^8, rm{M_{odot}}$, and 0.3% have at least one highly star-forming companion ($rm{SFR}>100,rm{M_{odot},yr^{-1}}$). Our results suggest that quasar-gas-rich companion galaxy systems are common phenomena in the early Universe and the high incidence of companions makes the study of such systems crucial to understand the growth and hierarchical build-up of galaxies and black holes.
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