Italy's emigration was huge, although not as much as Britain's or Germany's.
Italian mass emigration was a later phenomenon than Germany or Ireland's with only 550,000 Italians having left the country between 1789 and 1871, with half of these going to South America (mostly Argentina), though in absolute numbers it was larger. Italy had a massive emigration of 29 million between 1870 and 1985, the difference was that much of this was overwhelmingly male (77%) and temporary in nature, with many in this number being counted more than once. The total net migration out of Italy was nearly 19 million, a huge number by any standard.
Over half of the net (permanent) migration occurred in the 30 years preceding Italy's entry into World War I. The largest periods of net migration were as follows:
Largest periods of Net Migration from Italy
1861-1885 1,900,000
1886-1915 7,937,000
1916-1930 2,607,000
1946-1970 2,992,000
Germany had a net of 6.5 million emigrants to the Americas between 1700 and 1913, and another 2 million between 1914 and 1970. The vast majority went to the United States and came earlier than the Italians, so the number of people with German ancestry will be larger. However, the question is how many have only partial German ancestry, the number seems to be unclear in the United States as in 1980 it stood at 49 million, and jumped to 57 million in 1990 falling to under 43 million in 2000.
In South America there are no official numbers on ethnicity or inquiries to ancestry on census and some of the estimated numbers are vastly overstated and must be taken with a grain of salt. For instance, 250,000 Germans settled in Brazil between 1824 and 1969 and I have seen estimates of 5-7 million people of German ancestry in Brazil. Argentina likewise took in some 200,000 German immigrants between 1857 and 1959 and I see numbers of 3.5 million people with German ancestry listed, again probably a gross exaggeration. Australia too in similar numbers of Germans before 1914, and far more after World War II than either Brazil or Argentina, and people with German ancestry number 900,000 there by comparison.
Ireland too as had an estimated 9 to 11 million emigrate since 1700, with the majority going to North America (including the Caribbean), Great Britain, and Australia with smaller numbers going to South Africa, New Zealand, Argentina. Again as the bulk of this emigration was earlier than the Italy's, the number of people claiming an Irish ancestor will be larger. Between 1850 and 1913 alone some 4.5 million Irish emigrated.
Also important is the early emigration from the Iberian Peninsula and England to the Americas shown below and would account for such large diaspora populations.
Emigration from Europe Overseas
Before 1580
Portugal 330,000 (17% of 1580 population)
Spain 139,000 (1.85% of 1580 population)
Emigration from Europe Overseas
1580-1640
Portugal 360,000 (18% of 1600 population)
Spain 188,000 (2.4% of 1600 population)
Britain & Ireland 126,000 (2.6% of 1600 population)
France 4,000 (0.02% of 1600 population)
Netherlands 2,000 (0.1% of 1600 population)
1640-1700
Britain & Ireland 248,000 (4.1% of 1700 population)
Spain 158,000 (3.1% of 1700 population)
Portugal 150,000 (7.1% of 1700 population)
France 23,000 (0.1% of 1700 population)
Netherlands 13,000 (0.68% of 1700 population)
1700-1760
Portugal 600,000 (26% of 1760 population)
Britain & Ireland 372,000 (5.6% of 1760 population)
Spain 193,000 (2.1% of 1760 population)
Germany 97,000 (0.5% of 1760 population)
France 27,000 (0.1% of 1760 population)
Netherlands 5,000 (0.19% of 1760 population)
1760-1820
Britain & Ireland 615,000 (3% of 1820 population)
Portugal 105,000 (3.5% of 1820 population)
Spain 70,000 (0.6% of 1820 population)
Germany 51,000 (0.19% of 1820 population)
France 20,000 (0.07% of 1820 population)
Netherlands 5,000 (0.2% of 1820 population)