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We prove the existence of an almost surely asymptotic degree distribution, with stretched exponential decay; more precisely, the proportion of vertices of degree<jats:italic>d<\/jats:italic>tends to some positive number<jats:italic>c<\/jats:italic><jats:sub><jats:italic>d<\/jats:italic><\/jats:sub>&amp;gt; 0 almost surely as the number of steps goes to \u221e, and<jats:italic>c<\/jats:italic><jats:sub><jats:italic>d<\/jats:italic><\/jats:sub>~ (e\u03c0)<jats:sup>1\/2<\/jats:sup><jats:italic>d<\/jats:italic><jats:sup>1\/4<\/jats:sup>e<jats:sup>-2\u221a<jats:italic>d<\/jats:italic><\/jats:sup>holds as<jats:italic>d<\/jats:italic>\u2192 \u221e.<\/jats:p>","DOI":"10.1017\/s0021900200012523","type":"journal-article","created":{"date-parts":[[2016,3,30]],"date-time":"2016-03-30T20:26:30Z","timestamp":1459369590000},"page":"375-390","source":"Crossref","is-referenced-by-count":3,"title":["Asymptotic Properties of a Random Graph with Duplications"],"prefix":"10.1017","volume":"52","author":[{"given":"\u00c1gnes","family":"Backhausz","sequence":"first","affiliation":[]},{"given":"Tam\u00e1s F.","family":"M\u00f3ri","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,3,30]]},"reference":[{"key":"S0021900200012523_ref19","first-page":"297","volume-title":"Random Graphs '85","volume":"33","year":"1987"},{"key":"S0021900200012523_ref20","volume-title":"Random graphs and complex networks"},{"key":"S0021900200012523_ref17","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/42.3-4.425"},{"key":"S0021900200012523_ref16","volume-title":"Probability","year":"1996"},{"key":"S0021900200012523_ref15","doi-asserted-by":"crossref","first-page":"1290","DOI":"10.1214\/EJP.v14-653","volume":"14","year":"2009","journal-title":"Electron. 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