The WW-LDS site (http://talks.mormon.org/ww-lds.htm) gives some interesting data about the growth of the Church in Argentina in the last two decades.
1) Growth in Argentina has been strong and steady in the last twenty years, no period of sharp growth and then decreased growth as you find for Guatemala or Portugal, for example. The one period of slow growth was from 1982 to 1984 when (at least according to the Church News statistics), there were only about eight baptisms per mission per month. The following chart shows the membership for Argentina in each year since 1976:
1976 1978 1980 1982 1984 1986 1988 1990 1992 30,020 39,270 60,972 78,220 79,212 103,000 114,000 153,000 182,000 1994 1996 205,000 235,0002) As the following chart shows, during the 1980s membership growth in Argentina was only about 1/2 to 2/3 as much as the rest of South America. Since the last 1980s, however, membership growth in South America as a whole has slowed somewhat, and the rate in Argentina has increased to nearly the South American average. Likewise, growth in Argentina was only slightly higher than the worldwide average through most of the 1980s, but has been increasing at roughly twice the worldwide rate since then.
Percent growth in members (eg. 1.30 = 30% growth during four year period)
Years %80-84 %84-88 %88-92 %92-96 Argentina 1.30 1.44 1.60 1.29 South America 1.72 1.69 1.60 1.32 World 1.19 1.42 1.25 1.153) The increased growth since the late 1980s, however, might in part be a function of the large population of Argentina (along with Colombia, the most populous Spanish-speaking country in South America, with 34 million inhabitants in 1996), and the large number of missions (ten; as opposed to seven for the next highest Spanish-speaking countries, Peru and Chile). When current growth is measured as a function of the number of baptisms per month per mission, however, Argentina lags behind all of the other South American countries except Venezuela. The South American average is 208 baptisms per mission per month during the period 1990-96, whereas in Argentina it is only 130. This is somewhat higher than the worldwide average (104 per mission), but is of course much higher than more "modest-growth" countries like Japan (22 baptisms) or England (9 baptisms).
4) One way to measure to measure Church activity in a country might be by seeing how many members are in each stake, the idea being that the more active the members and the stronger the leadership base, the fewer numbers in each stake (cf. US 3940 members per stake, Europe 4118, Asia 5961, Caribbean 10,800). If this is true, then Argentina is just about at the norm compared with the rest of South America. Its 1996 figure of 5109 members per stake is higher than the the average for South America (which has an average of 4692), but it is still ahead of countries like Paraguay, Ecuador, or Colombia, which have 6000 or more members per stake.
5) As far as the percentage of people in Argentina that are LDS, the average is just a bit higher than the average for South America as a whole. The percent of the population that is LDS is 0.68%, or one in 146 people (compare this to Chile: one in 36, Ecuador: one in 52, all of SA: one in 164).
6) An article from the April 17, 1993 Church News (http://www.ldschurchnews.com/cgi-bin/libstory_church?dn_all&9304170061) gives some interesting insight into the current growth in Argentina, some of the challenges that missionaries there face, and its potential for future growth.
"Pres. Anthony I. Bentley of the Argentina Buenos Aires North Mission, observed: .... "Mission and stake leaders in Argentina today seek new ways to carry the gospel to the millions of the people who live in the great cities. Missionaries no longer go door to door because modern urban life no longer permits this form of proselyting. In the cities, many people dwell in buildings with electric security doors. Others fear opening doors to strangers. In addition, many homes are vacant in the day as people work long hours, or attend school."
"In reality, we are just commencing. The day will come when the members of the Church will represent a high percentage of the population of Argentina. The Church will be well-known and its members very respected. The influence of the Church will be beneficial and will be felt throughout the land."