I have done genealogical research on most Tossavainen family branches and unofficially coordinated paternal line DNA testing. Since 2017, I have had a more official role on the board of the Tossavainen Family Association.
The earliest known residence of the family is Tossavalansaari (meaning Tossavala's Island—nowadays a peninsula on Lake Syvänsi) in Pieksämäki (former Jäppilä municipality), which dates back to documents from the 1540s. The earliest known ancestor is Heikki Tossavainen, whose name has been passed only orally and as a place name, Heikinmäki (meaning Heikki's hill).
Known family branches (at least):
Petäjämäki village in Keitele: The descendants of Pekka Tossavainen (c. 1688–1770) form an extensive family, which has expanded not only in Keitele but also to other places such as Pielavesi, Kiuruvesi, Pihtipudas, and Pyhäjärvi. Pekka's ancestors originally lived further south in Vuonamonlahti village, and according to tax records, the Tossavainen family has been residing in the area since 1561.
Rautalampi: The descendants of Antti Tossavainen (1670–1736), the clerk of Rautalampi, have spread to the nearby areas of Suonenjoki and Vesanto. The first name suggests that Antti originated from Kuivaniemi village in Pielavesi.
In Kerkonkoski village in Rautalampi, there was another separate branch of the Tossavainen family during the 18th century. This branch has died out in the paternal line.
Kuivaniemi village in Pielavesi: The Tossavainen family by Lake Nikakka was divided into several different branches in the early 1600s. Later, in the early 1800s, a branch separated from Hemmola and settled in Kortekylä, Kiuruvesi. Tossavainen family members have been living in the Kuivaniemi area since 1555.
Riitlampi in present Tervo (or Kanala in Mäkikylä, Pyhäjärvi)
Leppävirta/Nilsiä
Västinniemi in Muuruvesi
Kasurila village in Siilinjärvi
Ilomantsi
Tohmajärvi
Pielisjärvi
Muurasjärvi village in Pihtipudas
In addition, many people have had Tossavainen or Tossava family names in the Oulu and Tornio regions. There is no information about their connection to the Tossavainen family branches in Savonia or Karelia.
You can also find Tossavainen family, who moved as Forest Finns in the Swedish–Norwegian region in the early 17th century and further to New Sweden, present Delaware state in the United States.
Malinen, P. (1993). Tossavaisia Tossavalansaaresta. [P. Malinen]